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## Course: 8th grade   >   Unit 1

• Scientific notation word problem: red blood cells
• Scientific notation word problem: U.S. national debt
• Scientific notation word problem: speed of light
• Numbers and operations: FAQ

## Scientific notation word problems

Chapter 6: Polynomials

## 6.3 Scientific Notation (Homework Assignment)

Scientific notation is a convenient notation system used to represent large and small numbers. Examples of these are the mass of the sun or the mass of an electron in kilograms. Simplifying basic operations such as multiplication and division with these numbers requires using exponential properties.

Scientific notation has two parts: a number between one and nine and a power of ten, by which that number is multiplied.

$\text{Scientific notation: }a \times 10^b, \text{ where }1 \le a \le 9$

The exponent tells how many times to multiply by 10. Each multiple of 10 shifts the decimal point one place. To decide which direction to move the decimal (left or right), recall that positive exponents means there is big number (larger than ten) and negative exponents means there is a small number (less than one).

Example 6.3.1

Convert 14,200 to scientific notation.

$\begin{array}{rl} 1.42&\text{Put a decimal after the first nonzero number} \\ \times 10^4 & \text{The exponent is how many times the decimal moved} \\ 1.42 \times 10^4& \text{Combine to yield the solution} \end{array}$

Example 6.3.2

Convert 0.0028 to scientific notation.

$\begin{array}{rl} 2.8&\text{Put a decimal after the first nonzero number} \\ \times 10^{-3}&\text{The exponent is how many times the decimal moved} \\ 2.8\times 10^{-3}&\text{Combine to yield the solution} \end{array}$

Example 6.3.3

Convert 3.21 × 10 5 to standard notation.

Starting with 3.21, Shift the decimal 5 places to the right, or multiply 3.21 by 10 5 .

321,000 is the solution.

Example 6.3.4

Convert 7.4 × 10 −3 to standard notation

Shift the decimal 3 places to the left, or divide 6.4 by 10 3 .

0.0074 is the solution.

Working with scientific notation is easier than working with other exponential notation, since the base of the exponent is always 10. This means that the exponents can be treated separately from any other numbers. For instance:

Example 6.3.5

Multiply (2.1 × 10 −7 )(3.7 × 10 5 ).

First, multiply the numbers 2.1 and 3.7, which equals 7.77.

Second, use the product rule of exponents to simplify the expression 10 −7 × 10 5 , which yields 10 −2 .

Combine these terms to yield the solution 7.77 × 10 −2 .

Example 6.3.6

(4.96 × 10 4 ) ÷ (3.1 × 10 −3 )

First, divide: 4.96 ÷ 3.1 = 1.6

Second, subtract the exponents (it is a division): 10 4− −3 = 10 4 + 3 = 10 7

Combine these to yield the solution 1.6 × 10 7 .

For questions 1 to 6, write each number in scientific notation.

For questions 7 to 12, write each number in standard notation.

• 2.56 × 10 2

For questions 13 to 20, simplify each expression and write each answer in scientific notation.

• (7 × 10 −1 )(2 × 10 −3 )
• (2 × 10 −6 )(8.8 × 10 −5 )
• (5.26 × 10 −5 )(3.16 × 10 −2 )
• (5.1 × 10 6 )(9.84 × 10 −1 )
• $\dfrac{(2.6 \times 10^{-2})(6 \times 10^{-2})}{(4.9 \times 10^1)(2.7 \times 10^{-3})}$
• $\dfrac{(7.4 \times 10^4)(1.7 \times 10^{-4})}{(7.2 \times 10^{-1})(7.32 \times 10^{-1})}$
• $\dfrac{(5.33 \times 10^{-6})(9.62 \times 10^{-2})}{(5.5 \times 10^{-5})^2}$
• $\dfrac{(3.2 \times 10^{-3})(5.02 \times 10^0)}{(9.6 \times 10^3)^{-4}}$

## The Math You Need, When You Need It

math tutorials for students majoring in the earth sciences

## Scientific Notation - Practice Problems

Solving earth science problems with scientific notation, × div[id^='image-'] {position:static}div[id^='image-'] div.hover{position:static} introductory problems.

These problems cover the fundamentals of writing scientific notation and using it to understand relative size of values and scientific prefixes.

Problem 1: The distance to the moon is 238,900 miles. Write this value in scientific notation.

Problem 2: If one mile is 1609.34 meters. What the distance to the moon in meters using scientific notation.

1609.34 m/(mi) xx 238","900  mi = 384,400,000 m

Notice in the above unit conversion the 'mi' units cancel each other out because 'mi' is in the denominator for the first term and the numerator for the second term

Problem 4: The atomic radius of a magnesium atom is approximately 1.6 angstroms, which is equal to 1.6 x 10 -10 meters (m). How do you write this length in standard form?

0.00000000016 m

Fissure A = 40,0000 m Fissure B = 5,0000 m

This shows fissure A is larger (by almost 10 times!). The shortcut to answer a question like this is to look at the exponent. If both coefficients are between 1-10, then the value with the larger exponent is the larger number.

Problem 6: The amount of carbon in the atmosphere is 750 petagrams (pg). One petagram equals 1 x 10 15 grams (g). Write out the amount of carbon in the atmosphere in (i) scientific notation and (ii) standard decimal format.

The exponent is a positive number, so the decimal will move to the right in the next step.

750,000,000,000,000,000 g

Scientific notation is used in solving these earth and space science problems and they are provided to you as an example. Be forewarned that these problems move beyond this module and require some facility with unit conversions, rearranging equations, and algebraic rules for multiplying and dividing exponents. If you can solve these, you've mastered scientific notation!

Problem 7: Calculate the volume of water (in cubic meters and in liters) falling on a 10,000 km 2 watershed from 5 cm of rainfall.

10,000  km^2 = 1 xx 10^4  km^2

5 cm of rainfall = 5 xx 10^0 cm

Let's start with meters as the common unit and convert to liters later. There are 1 x 10 3 m in a km and area is km x km (km 2 ), therefore you need to convert from km to m twice:

1 xx 10^3 m/(km) * 1 xx 10^3 m/(km) = 1 xx 10^6 m^2/(km)^2 1 xx 10 m^2/(km)^2 * 1 xx 10^4 km^2 = 1 xx 10^10 m^2 for the area of the watershed.

For the amount of rainfall, you should convert from centimeters to meters:

5 cm * (1 m)/(100 cm)= 5 xx 10^-2 m

V = A * d

When multiplying terms with exponents, you can multiply the coefficients and add the exponents:

V = 1 xx 10^10 m^2 * 5.08 xx 10^(-2) m = 5.08 xx 10^8 m^3

Given that there are 1 x 10 3 liters in a cubic meter we can make the following conversion:

1 xx 10^3 L * 5.08 xx 10^8 m^3 = 5.08 xx 10^11 L

V = 4/3 pi r^3

Using this equation, plug in the radius (r) of the dust grains.

V = 4/3 pi (2 xx10^(-6))^3m^3

Notice the (-6) exponent is cubed. When you take an exponent to an exponent, you need to multiply the two terms

V = 4/3 pi (8 xx10^(-18)m^3)

Then, multiple the cubed radius times pi and 4/3

V = 3.35 xx 10^(-17) m^3

m = 3.35 xx 10^(-17) m^3 * 3300 (kg)/m^3

Notice in the equation above that the m 3 terms cancel each other out and you are left with kg

m = 1.1 xx 10^(-13) kg

V = 4/3 pi (2.325 xx10^(15) m)^3

V = 5.26 xx10^(46) m^3

Number of dust grains = 5.26 xx10^(46) m^3 xx 0.001 grains/m 3

Number of dust grains = 5.26xx10^43 "grains"

Total mass = 1.1xx10^(-13) (kg)/("grains") * 5.26xx10^43 "grains"

Notice in the equation above the 'grains' terms cancel each other out and you are left with kg

Total mass = 5.79xx10^30 kg

If you feel comfortable with this topic, you can go on to the assessment . Or you can go back to the Scientific Notation explanation page .

« Previous Page       Next Page »

## Module 12: Exponents

Problem solving with scientific notation, learning outcomes.

• Solve application problems involving scientific notation

Water Molecule

## Solve application problems

Learning rules for exponents seems pointless without context, so let’s explore some examples of using scientific notation that involve real problems. First, let’s look at an example of how scientific notation can be used to describe real measurements.

Match each length in the table with the appropriate number of meters described in scientific notation below.

Red Blood Cells

One of the most important parts of solving a “real” problem is translating the words into appropriate mathematical terms, and recognizing when a well known formula may help. Here’s an example that requires you to find the density of a cell, given its mass and volume. Cells aren’t visible to the naked eye, so their measurements, as described with scientific notation, involve negative exponents.

Human cells come in a wide variety of shapes and sizes. The mass of an average human cell is about $2\times10^{-11}$ grams [1] Red blood cells are one of the smallest types of cells [2] , clocking in at a volume of approximately $10^{-6}\text{ meters }^3$. [3] Biologists have recently discovered how to use the density of some types of cells to indicate the presence of disorders such as sickle cell anemia or leukemia. [4]  Density is calculated as the ratio of $\frac{\text{ mass }}{\text{ volume }}$. Calculate the density of an average human cell.

Read and Understand:  We are given an average cellular mass and volume as well as the formula for density. We are looking for the density of an average human cell.

Define and Translate:   $m=\text{mass}=2\times10^{-11}$, $v=\text{volume}=10^{-6}\text{ meters}^3$, $\text{density}=\frac{\text{ mass }}{\text{ volume }}$

Write and Solve:  Use the quotient rule to simplify the ratio.

$\begin{array}{c}\text{ density }=\frac{2\times10^{-11}\text{ grams }}{10^{-6}\text{ meters }^3}\\\text{ }\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=2\times10^{-11-\left(-6\right)}\frac{\text{ grams }}{\text{ meters }^3}\\\text{ }\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=2\times10^{-5}\frac{\text{ grams }}{\text{ meters }^3}\\\end{array}$

If scientists know the density of healthy cells, they can compare the density of a sick person’s cells to that to rule out or test for disorders or diseases that may affect cellular density.

The average density of a human cell is $2\times10^{-5}\frac{\text{ grams }}{\text{ meters }^3}$

The following video provides an example of how to find the number of operations a computer can perform in a very short amount of time.

Light traveling from the sun to the earth.

In the next example, you will use another well known formula, $d=r\cdot{t}$, to find how long it takes light to travel from the sun to the earth. Unlike the previous example, the distance between the earth and the sun is massive, so the numbers you will work with have positive exponents.

The speed of light is $3\times10^{8}\frac{\text{ meters }}{\text{ second }}$. If the sun is $1.5\times10^{11}$ meters from earth, how many seconds does it take for sunlight to reach the earth?  Write your answer in scientific notation.

Read and Understand:  We are looking for how long—an amount of time. We are given a rate which has units of meters per second and a distance in meters. This is a $d=r\cdot{t}$ problem.

Define and Translate:

$\begin{array}{l}d=1.5\times10^{11}\\r=3\times10^{8}\frac{\text{ meters }}{\text{ second }}\\t=\text{ ? }\end{array}$

Write and Solve:  Substitute the values we are given into the $d=r\cdot{t}$ equation. We will work without units to make it easier. Often, scientists will work with units to make sure they have made correct calculations.

$\begin{array}{c}d=r\cdot{t}\\1.5\times10^{11}=3\times10^{8}\cdot{t}\end{array}$

Divide both sides of the equation by $3\times10^{8}$ to isolate  t.

$\begin{array}{c}1.5\times10^{11}=3\times10^{8}\cdot{t}\\\text{ }\\\frac{1.5\times10^{11}}{3\times10^{8}}=\frac{3\times10^{8}}{3\times10^{8}}\cdot{t}\end{array}$

On the left side, you will need to use the quotient rule of exponents to simplify, and on the right, you are left with  t.

$\begin{array}{c}\frac{1.5\times10^{11}}{3\times10^{8}}=\frac{3\times10^{8}}{3\times10^{8}}\cdot{t}\\\text{ }\\\left(\frac{1.5}{3}\right)\times\left(\frac{10^{11}}{10^{8}}\right)=t\\\text{ }\\\left(0.5\right)\times\left(10^{11-8}\right)=t\\0.5\times10^3=t\end{array}$

This answer is not in scientific notation, so we will move the decimal to the right, which means we need to subtract one factor of $10$.

$0.5\times10^3=5.0\times10^2=t$

The time it takes light to travel from the sun to the earth is $5.0\times10^2=t$ seconds, or in standard notation, $500$ seconds.  That’s not bad considering how far it has to travel!

Scientific notation was developed to assist mathematicians, scientists, and others when expressing and working with very large and very small numbers. Scientific notation follows a very specific format in which a number is expressed as the product of a number greater than or equal to one and less than ten, and a power of $10$. The format is written $a\times10^{n}$, where $1\leq{a}<10$ and n is an integer. To multiply or divide numbers in scientific notation, you can use the commutative and associative properties to group the exponential terms together and apply the rules of exponents.

## Contribute!

• Orders of magnitude (mass). (n.d.). Retrieved May 26, 2016, from https://en.wikipedia.org/wiki/Orders_of_magnitude_(mass) ↵
• How Big is a Human Cell? ↵
• How big is a human cell? - Weizmann Institute of Science. (n.d.). Retrieved May 26, 2016, from http://www.weizmann.ac.il/plants/Milo/images/humanCellSize120116Clean.pdf ↵
• Grover, W. H., Bryan, A. K., Diez-Silva, M., Suresh, S., Higgins, J. M., & Manalis, S. R. (2011). Measuring single-cell density. Proceedings of the National Academy of Sciences, 108(27), 10992-10996. doi:10.1073/pnas.1104651108 ↵
• Application of Scientific Notation - Quotient 1 (Number of Times Around the Earth). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/15tw4-v100Y . License : CC BY: Attribution
• Application of Scientific Notation - Quotient 2 (Time for Computer Operations). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/Cbm6ejEbu-o . License : CC BY: Attribution
• Screenshot: water molecule. Provided by : Lumen Learning. License : CC BY: Attribution
• Screenshot: red blood cells. Provided by : Lumen Learning. License : CC BY: Attribution
• Screenshot: light traveling from the sun to the earth. Provided by : Lumen Learning. License : CC BY: Attribution
• Unit 11: Exponents and Polynomials, from Developmental Math: An Open Program. Provided by : Monterey Institute of Technology and Education. Located at : http://nrocnetwork.org/resources/downloads/nroc-math-open-textbook-units-1-12-pdf-and-word-formats/ . License : CC BY: Attribution

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## HiSET: Math : Solve problems using scientific notation

Study concepts, example questions & explanations for hiset: math, all hiset: math resources, example questions, example question #1 : solve problems using scientific notation.

Simplify the following expression using scientific notation.

You can solve this problem in several ways. One way is to convert each number out of scientific notation and write it out fully, then find the sum of the two values and convert the answer back into scientific notation.

Another, potentially faster, way to solve this problem is to convert one answer into the same scientific-notational terms as the other and then sum them.

## Example Question #2 : Solve Problems Using Scientific Notation

Multiply, and express the product in scientific notation:

Convert 7,200,000 to scientific notation as follows:

Move the (implied) decimal point until it is immediately after the first nonzero digit (the 7). This required moving the point six units to the left:

Rearrange and regroup the expressions so that the powers of ten are together:

Multiply the numbers in front. Also, multiply the powers of ten by adding exponents:

In order for the number to be in scientific notation, the number in front must be between 1 and 10. An adjustment must be made by moving the implied decimal point in 36 one unit left. It follows that

the correct response.

## Example Question #3 : Solve Problems Using Scientific Notation

Express the product in scientific notation.

None of the other choices gives the correct response.

Scientific notation refers to a number expressed in the form

Each factor can be rewritten in scientific notation as follows:

Now, substitute:

Apply the Product of Powers Property:

This is in scientific notation and is the correct choice.

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## Chemical Measurement Unit Plan Mark as Favorite (105 Favorites)

LESSON PLAN in Density , Percent Composition , Accuracy , Dimensional Analysis , Measurements , Scientific Notation , Significant Figures , SI Units , Unlocked Resources , Unit Plans . Last updated September 23, 2020.

The AACT High School Classroom Resource library and multimedia collection has everything you need to put together a unit plan for your classroom: lessons, activities, labs, projects, videos, simulations, and animations. We constructed a unit plan for introducing the concepts needed for students to collect and use chemical measurements:Percent Composition, Metric Units, Accuracy and Precision, Percent Error, Density, Scientific Notation, Significant Figures, and Unit Conversion. These math based topics are very important for your students to master before they dig into other chemistry concepts.This unit is designed to be used at beginning of the school year. You may want to leave activities out, based on the math abilities of your incoming students and the level of the class.

High School

By the end of this unit, students should be able to

• Critically analyze a given problem, and complete appropriate calculations for mass and volume.
• Define percent composition.
• Calculate the percent composition of a substance in a sample.
• Take measurements using metric units.
• Determine the accuracy of different pieces of glassware.
• Accurately use laboratory equipment to gather data.
• Explain why some pieces of glassware produce better accuracy than others.
• Construct and analyze a line graph using Excel.
• Determine a method to measure the mass and volume of an irregular object.
• Calculate density and be able to explain why the density of an object does not change.
• Calculate the density of an irregular object using their data.
• Calculate the percentage error of their results using both the experimentally determined value and the accepted value for density.
• Convert very large and very small values into proper scientific notation.
• Recognize the benefit of using scientific notation to solve large scale problems.
• Use dimensional analysis for mass, length, volume, temperature, and density unit conversion problems.
• Convert between units of measurement using dimensional analysis.
• Understand the purpose of using dimensional analysis for converting between units of measurement.
• Use lab equipment to measure volume, mass, and length to the correct number of significant figures.

## Chemistry Topics

This unit supports students’ understanding of

• Measurement

Percent Composition

• Dimensional Analysis

Metric Units

• Accuracy and Precision
• Percent Error

Scientific Notation

Significant Figures

Unit Conversion

Teacher Preparation : See individual resources.

Lesson : 10 - 15 class periods, depending on class level.

• Refer to the materials list given with each individual activity.
• Refer to the safety instructions given with each individual activity.

## Teacher Notes

• The activities shown below are listed in the order that they should be completed.
• The teacher notes, student handouts, and additional materials can be accessed on the page for each individual activity.
• Please note that most of these resources are AACT member benefits.

## Classroom Resources

• "Keys for Success in Teaching Chemistry: Imagination and Resourcefulness ": Before you begin the unit, take a few minutes to read this article from our March 2016 issue of Chemistry Solutions . This article discusses several labs that the author uses to help teach his students to be creative and resourceful when collecting and using lab data.
• Mineral Investigation: Start your year off with this great introductory lab that familiarizes students with data collection and manipulation while also incorporating engineering principles and guided inquiry.In this lab, students put their problem solving skills to work as a team to determine how many specific samples of ore can be made from a lode equivalent to the size of their classroom using percent composition. This lab is perfect for the start of the school year to engage students in real-life applications of chemistry, as well as essential mathematic and measurement skills. You can then choose from one of these two labs to give your students more practice with percent composition calculations.
• Percent Composition of Bubble Gum : In this lab students determine the amount of sweetener in various brands of gum by determining the mass difference of the gum before and after it is chewed.By the end of this lesson, students should be able to define and calculate percent composition.
• Percent Composition : In this lab students calculate the percent composition of sugar in gum and the percent composition of water in popcorn kernels.By the end of this lab, students should be able to calculate the percent composition of a substance in a sample.
• Mysteriously Melodramatic & Maniacal Metric Measurements : Introduce the metric system and units with this activity, which asks students to predict the measurements of objects using metric units. They then take the actual measurements and compare them to their predictions.This activity works well as a competition, assigning points for teams based on how closely their predictions match actual measurements.

Accuracy, Precision, and Percent Error

• Measuring Volume : This simulation shows students an image of a graduated cylinder and asks them to report an accurate volume measurement with the correct number of significant figures. They then are asked to determine the uncertainty value of the graduated cylinder. The simulation includes several different sizes of graduated cylinders, each containing unique markings, so students will be challenged to analyze each individually.
• Glassware Accuracy : Follow the simulation with this laboratory activity, which allows students to further explore the concepts of accuracy, precision, and percent error with this lab.Students use different types of laboratory glassware to measure 50 mL of water and determine the accuracy of each piece of glassware.By the end of this lesson, students should be able to determine the accuracy of different pieces of glassware and calculate percent error.
• The Chemistry Composition Challenge : Your students will be challenged to design a method to solve three chemistry problems with this lab. One problem requires students to determine the thickness of a piece of aluminum foil and compare their value to the actual one. Another has them determine the identity of an unknown metal by calculating its density. This resource includes extensive teacher notes to help you guide your students through this inquiry activity.
• Density Animation : Use this animation to introduce the concept of density and help your students visualize density on the particulate level. There are opportunities to make qualitative and quantitative comparisons between substances.
• Density : You can then use this lab to allow your students to determine the density of several liquids and solids. They then identify an unknown metal by determining its density and calculate the percent error within the class for a specific sample.By the end of this activity, students should be able to calculate the density of a liquid by measuring volume and mass, calculate the density of a solid using the displacement method for finding volume identify an unknown substance by determining its density, calculate percent error, and explain if their results are accurate or precise.
• Graphing Density : Finish up the topic of density with this lab, which requires students to collect data and use graphing to determine the density values of unknown metal samples. This activity will help your students learn to construct a line graph using Excel and analyze a linear equation to help determine density.
• Investigating the Density of an Irregular Solid Object Lab : If you think your students need another activity to solidify their understanding, try out this lab. Students use common laboratory equipment to devise a method to measure the density of several irregular objects. They will then create a formal laboratory report using both their own data and data from the entire class. Read an article about this activity in the September 2016 issue of Chemistry Solutions .
• Use the lab, Colors of the Rainbow to assess your students’ understanding of the concept of density. In this lab, students calculate the density of several unknown liquids and then use their findings to build a density column. There are eight unknown solutions that are grouped nine different ways so that each of the lab groups will have a unique combination of liquids to build their density column.
• "Bringing Real-Life Context to Chemical Math ": Before moving on to the topic of scientific notation, read this article in the March 2016 issue of Chemistry Solutions .
• Scientific Notation: Then use this activity to introduce the topic to your students.Students have a button, which they move like a decimal point, to be actively involved in putting numbers into and taking numbers out of scientific notation format.
• Using Scientific Notation in Chemistry : Follow up with this lesson, which has students solve a variety of real-world problems using scientific notation. Students listen to a convoluted radio conversation about coffee which will relate to a math-based problem that this lesson is developed around. Students begin to recognize the benefits of using scientific notation in their calculations.This lesson includes a formative quiz, summative quiz, slides, and a radio conversation on YouTube
• The Significant Figures and Lab Data : Many students seem to struggle with significant figures, especially when it is taught out of context.This activity allows students to use laboratory equipment of different precision to collect data for several different metals, and then use the data to calculate the density of each.They then compare their calculated densities to accepted values and determine the combination of equipment that leads to the most accurate calculation of density.
• The Measurement Animation allows students to review the fundamentals of measurement in length, mass, and volume. Various units of measurement will be presented for comparison, and several conversion calculations will be demonstrated using dimensional analysis.
• The Temperature Guys : Open your discussion of unit conversion with this video from our Founders of Chemistry series.It tells the story of how temperature as we currently know it evolved. The first thermometers invented in the early 1600s are very different than ones we use today! An activity sheet that includes question for students to answer as they watch the video is available to download.
• Dimensional Analysis and Unit Conversion : Follow the video with this lesson plan to introduce the process of unit conversion.This resource includes a PowerPoint Presentation and student handout with practice problems.
• The activity, Dimensional Analysis with Notecards is a great resource to help students who are struggling with this important concept. This activity allows them to visualize dimensional analysis using pre-made conversion factors on notecards and understand the importance of cancelling units to solve conversion problems.
• Unit Conversion Online Tutorial : Next, use this activity to have your students interact with a web-based tutorial that uses a drag and drop interface in order to learn how to convert between units of measurement using dimensional analysis. The tutorial allows students to learn at their own pace, and also provides feedback while they are solving problems.You may want to read the March 2016 issue of Chemistry Solutions article, "A Student-Centered, Web-Based Approach to Teaching Unit Conversions " before using the activity.
• Math and Measurement : Get your students ready for a unit assessment with this lab, which allows students to practice introductory math skills that will be used in chemistry all year. This includes metric conversion, significant figures, scientific notation, dimensional analysis, density, percent error, accuracy and precision, as well as using lab equipment.
• Nanoscale & Self-Assembly : An option for an advanced culminating lab or extension for the unit could be this lab, which incorporates measurements, and dimensional analysis.In this activity, students determine both the diameter of one single BB and the length of an oleic acid molecule using simple measurements and volume/surface area relationships.
• ChemMatters : If you’d like to increase your students’ scientific literacy while connecting dimensional analysis to the real world, have them read “Recycling Aluminum: A Way of Life or a Lifestyle?” from the April 2012 magazine or “ Drivers, Start Your (Electric) Engines ” from the February 2013 issue.
• The lesson, Captivating Chemistry of Coins  will allow students to demonstrate their understanding of physical and chemical properties of matter by comparing the composition of different pennies. This is done by determining the density of pre- and post-1982 pennies which will be compared to the density of different metals. This lab is introduced with the ChemMatters article, The Captivating Chemistry of Coins .

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1. 30 Scientific Notation Word Problems Worksheet

2. Scientific Notation Word Problem Practice PLUS Spiral Review by Jessica

3. Scientific notation problem solving

4. Lesson 6 Problem Solving Practice

5. Scientific Notation Word Problems

6. Scientific Notation Practice Packet by Maisonet Math

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1. Intro to Scientific Notation

2. 6) Problem solving skills| Dimensional formulas

3. Chemistry: Math Basics and Scientific Notation

4. 8th Grade Math 2.4b, Multiplying with Scientific Notation

5. Scientific Notation

6. How To Write Scientific Notation #math #mathematics #scientificnotation

1. Scientific notation (practice)

Scientific notation (practice) | Khan Academy. 8th grade. Course: 8th grade > Unit 1. Lesson 10: Scientific notation intro. Scientific notation example: 0.0000000003457. Scientific notation examples. Scientific notation review. Math > 8th grade > Numbers and operations > Scientific notation intro. Google Classroom.

2. Unit 7: Exponents and scientific notation

Learn. Exponent properties with products. Exponent properties with quotients. Negative exponent intuition. Multiplying & dividing powers (integer exponents) Practice. Multiply powers. Start. Practice. Divide powers. Practice. Multiply & divide powers (integer exponents) Get 5 of 7 questions to level up! Practice. Lesson 8: Combining bases. Learn.

3. Scientific notation examples (video)

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 10^8. Created by Sal Khan and CK-12 Foundation. Created by Sal Khan and CK-12 Foundation.

4. Roots, exponents, & scientific notation

Learn. Intro to square roots. Square roots of perfect squares. Intro to cube roots. Worked example: Cube root of a negative number. Square root of decimal. Dimensions of a cube from its volume. Square roots review. Cube roots review. Practice. Up next for you: Square roots Get 5 of 7 questions to level up! Start.

5. PDF SSON 6 Using Scientific Notation

Using Scientific Notation. LESSON 6 . Using Scientific Notation. EXAMPLE A . Multiply: (3.5  103)(2  105). Express the answer in scientific notation. Multiplication is commutative and associative. Rearrange the factors and group the coeficients and powers of 10. (3.5  103)(2  105) 5 (3.5  2.0)(103  105) 2 Multiply the coeficients.

6. Scientific notation word problems (practice)

Google Classroom. You might need: Calculator. Light travels 9.45 \cdot 10^ {15} 9.45 ⋅ 1015 meters in a year. There are about 3.15 \cdot 10^7 3.15 ⋅107 seconds in a year. How far does light travel per second? Write your answer in scientific notation. meters. Show Calculator. Stuck? Review related articles/videos or use a hint. Report a problem. 7.

7. 6.3 Scientific Notation (Homework Assignment)

Scientific notation is a convenient notation system used to represent large and small numbers. Examples of these are the mass of the sun or the mass of an electron in kilograms. Simplifying basic operations such as multiplication and division with these numbers requires using exponential properties.

8. Scientific Notation

Problem 1: The distance to the moon is 238,900 miles. Write this value in scientific notation. Problem 2: If one mile is 1609.34 meters. What the distance to the moon in meters using scientific notation. Problem 3: The age of the Earth is roughly four billion and six hundred million years. Write this number in (i) standard decimal format, and ...

9. Scientific Notation: Practice Problems

In this lesson, review what scientific notation is and examine two practice problems that show how to use this notation easily. Updated: 10/21/2021. Scientific Notation. Do you know what the mass...

10. Problem Solving With Scientific Notation

Summary. Scientific notation was developed to assist mathematicians, scientists, and others when expressing and working with very large and very small numbers. Scientific notation follows a very specific format in which a number is expressed as the product of a number greater than or equal to one and less than ten, and a power of 10 10.

11. PDF Module 1

Answers: 943 = 943 x 1 = 943 x 100 = 9.43 x 102 in scientific notation. 0.00036 = 0.00036 x 100 = 3.6 x 10―4 in scientific notation. When a number is converted to scientific notation, numbers that are • larger than one have positive exponents (zero and above) in scientific notation;

12. Scientific Notation Calculator

How to solve your scientific notation problems. To solve your scientific notation problem, type in your number like 23400. The scientific notation calculator will then show you the steps to help you learn how to convert the number to scientific notation. Scientific Notation Video Lesson. Khan Academy Video: Scientific Notation Examples.

13. Math Practice Problems

1. 2223000000. 2. 0.000007505. Answers. Complexity=3, Mode=toNormal. Convert from scientific notation into normal notation. Complexity=4, Mode=toScientific. Convert from normal notation into scientific notation. Sample answer: 4.5 × 106. Type: 4.5 * 10^6. Learn more about our online math practice software . "MathScore works."

14. Lesson 6 Scientific Notation Classwork Practice.pdf

View Lesson 6 Scientific Notation Classwork Practice.pdf from MATH MISC at Baruch College, CUNY. NAME _ DATE _ PERIOD _ Lesson 6 Scientific Notation Classwork Practice Course 3 • Chapter 1 Real ... Lesson 6 Scientific Notation Classwork Practice.pdf - NAME ... Doc Preview. Pages 2. Total views 19. Baruch College, CUNY. MATH. MATH MISC ...

15. Lesson 6 Homework Practice Scientific Notation

Lesson 6 Homework Practice Scientific Notation Write each number in standard form. 1. 9.03 1022. 7.89 1033. 4.115 1054. 3.201 1065. 5.1 1026. 7.7 1057. 3.85 1048. 1.04 103Write each number in scientific. Fill & Sign Online, Print, Email, Fax, or Download. Get Form. We are not affiliated with any brand or entity on this form.

16. Solve problems using scientific notation

Academic Tutoring. » Solve problems using scientific notation. Simplify the following expression using scientific notation. It follows that 7,200,000 can be rewritten as. By similar reasoning, 5,000,000 can be rewritten as. Express the product in scientific notation. This is in scientific notation and is the correct choice.

17. Scientific Notation: Practice Problems

Quiz. Course. Try it risk-free for 30 days. Instructions: Choose an answer and hit 'next'. You will receive your score and answers at the end. question 1 of 3. What is the value of (2 x 10^6) + (3...

18. Scientific Notation Lesson Plan

Use Study.com's video lesson on scientific notation to practice the rules required to add, subtract, multiply and divide numbers that are written in scientific notation. End the lesson with a game...

19. Scientific Notation

This animated Math Shorts video from UEN explains the term scientific notation and provides several examples in converting extreme numbers to and from scientific notation. It also demonstrates how to multiply numbers using scientific notation. In the accompanying classroom activity, students practice writing numbers in scientific notation and develop real-world problems for each other to solve.

20. Scientific Notation Practice Worksheets & Teaching Resources

. Scientific Notation Practice Worksheets & Teaching Resources | TpT. Browse scientific notation practice resources on Teachers Pay Teachers, a marketplace trusted by millions of teachers for original educational resources. DID YOU KNOW: Seamlessly assign resources as digital activities. Learn how in 5 minutes with a tutorial resource.

21. Lesson 6 Homework Practice Scientific Notation Answer Key

Fill Lesson 6 Homework Practice Scientific Notation Answer Key, Edit online. Sign, fax and printable from PC, iPad, tablet or mobile with pdfFiller Instantly. Try Now! Home; For Business. ... Lesson 6 Homework Practice Scientific Notation Write each number in standard form. 1. 9.03 1022. 7.89 1033. 4.115 1054. 3.201 1065. 5.1 1026. 7.7 1057. 3. ...

22. Classroom Resources

Recognize the benefit of using scientific notation to solve large scale problems. Use dimensional analysis for mass, length, volume, temperature, and density unit conversion problems. Convert between units of measurement using dimensional analysis. Understand the purpose of using dimensional analysis for converting between units of measurement.

23. Scientific Notation Sample Problems

These sample problems below for Scientific Notation were generated by the MathScore.com engine. Sample Problems For Scientific Notation. Complexity=3, Mode=toNormal. Convert from scientific notation into normal notation. 1. 8.39 × 10 6. 2. 5.86 × 10 8. Complexity=4, Mode=toScientific. Convert from normal notation into scientific notation.