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Ordering Decimals: Definition, Types, Examples

What is ordering decimals, place values chart in decimals, different types of ordering, solved examples on ordering decimals, practice problems on ordering decimals, frequently asked questions on ordering decimals.

Arranging decimal numbers in a specific order, i.e, ascending or descending, on the basis of the place values is known as ordering decimals.

Decimals are numbers that have a whole number part and a fractional part divided by a decimal point. Decimals just like any other numbers can be compared and ordered in either ascending or descending order.

Add Decimals (Greater than 1) Using Model Game

Comparing and ordering decimals gets easier with the place value chart. The following image shows the place value chart in decimals.

Place value chart in decimals

Let’s understand the place values of decimals with an example. Consider the decimal number 1111.1111. Every place has the same digit. However, their place values are different!

Example of place values in decimals

Related Worksheets

Add and Subtract Decimals less than 1 with Regrouping: Horizontal Worksheet

Steps of Ordering Decimals

To order decimal numbers, we need to first learn how to compare decimal numbers. 

Step 1: Use the place value chart!

Write the decimals in the place value chart such that the place values of all the decimals are aligned. The empty boxes at the end of the decimal can be filled with zeroes.

Step 2: Compare the whole number part first.

Always start comparing the digits at the highest place value. Thus, the decimal having the greater whole number part is greater!

For example: Consider the decimals 12.5 and 15.2.

12 is less than 15

Thus, 15.2 is greater than 12.5.

Step 3: Compare the tenths!

 If the whole number part matches, compare the next place value, tenth.

Consider the decimals 1.5 and 1.4.

The whole number is 1 in both numbers, thus we will compare the digits after the decimal point—4 and 5.

Thus, $1.5 \gt 1.4$

Step 4: Compare the hundredths.

If the digits at the tenth place are the same, move to the next place value and compare the digits.

Example: Consider the decimals 23.56 and 23.53. 

We will write them in the place value chart for better understanding!

Comparing decimals

The part 23.5 is the same in both the decimals.

Thus, we compare the digits at the hundredths place, 3 and 6.

$3 \gt 6$ and hence 23.56 is greater than 23.53.

Once you compare the given decimals, ordering them is just the matter of arranging them in increasing or decreasing order.

There are two different types of the ordering of decimals:

  • Ascending order: The order of decimal numbers such that, in a sequence, each decimal number is not less than the previous number, or we can also say that the terms are either equal or greater than the previous number.
  • Descending order: The order of decimal numbers such that, in a sequence, each decimal number is not more than the previous number, or we can also say that the terms are either equal or lesser than the previous number.

How to Order Decimals

To order decimals, we will first compare the decimals. Write the decimals in the place value chart in order to compare them. To arrange them in ascending order, we write them from the smallest to the greatest. To arrange them in descending order, we write them from the greatest to the smallest.

Example 1: Order decimals from least to greatest. 

5.31, 6.88, 7.21, 6.45

Comparing and ordering decimals

Compare the digits at ones place: we get $7 \gt 6 \gt 5$

Thus, 7.21 is the greatest decimal and 5.31 is the smallest.

To compare 6.88 and 6.45, compare the digits at the tenths place.

Since $4 \lt 8$, we get $6.45 \lt 6.88$

Thus, $5.31 \lt 6.45 \lt 6.88 \lt 7.21$

The given decimals can be arranged in ascending order as: 5.31, 6.45, 6.88, 7.21

Ordering Decimals in Ascending Order

To order the decimal numbers in ascending order, we will arrange the numbers in such a way that each decimal number is smaller than the next decimal number. It means increasing order. How can we order decimals from least to greatest? Simply compare them using the place value chart and start listing them in the increasing order.

Ordering Decimals in Descending Order

To order the decimal numbers in descending order, we will arrange the numbers in such a way that each decimal number is larger than the next decimal number. It means decreasing order.

  • The decimal numbers are of three types—terminating, non-terminating repeating, and non-terminating non-repeating.
  • The terminating and non-terminating repeating decimal numbers are classified as rational numbers.
  • The non-terminating non-repeating decimal numbers are classified as irrational numbers.

This article gives an insight into the concept of decimals, teaching us how to compare decimals and how to arrange them in ascending or descending order. Ordering decimals is a part of daily life, which we see commonly while comparing amounts of some objects and the values are in decimal numbers.

1. Compare and arrange the following decimal numbers in descending order:

0.51, 0.45, 3.22, 1.67, 0.452.

Solution: 

Write the numbers in the place value chart. Start comparing the digits at the highest place value, that is, the ones place.

Comparing and ordering decimals

Comparing the ones place digits, we get

$1.67 \lt 3.22$

For the decimals 0.51, 0.45, and 0.452, we compare the tenths, hundredths, and thousandths place.

$0.51 \lt 0.450 \lt 0.452$

The numbers in descending order are:

$3.22 \gt 1.67 \gt 0.51 \gt 0.452 \gt 0.45$

2. Which one is greater—1.01 or 1.10?

Comparing and ordering decimals example

The numbers 1.01 and 1.10 both have the same whole number part 1.

We will compare the digits at the tenths place, which are 0 and 1.

Thus $1.10 \gt 1.01$.

3. Arrange the given decimals in ascending order.

0.96, 6.01, 0.0009, 0.93

Solution: Start comparing the digits at the highest place value.

We get that 6.01 is the greatest decimal.

Between 0.96, 0.93 and 0.0009, we get

$0.93 \lt 0.96 \lt 0.0009$

Thus, the given decimals can be written in the ascending order as:

$0.93 \lt 0.96 \lt 0.0009 \lt 6.01$

Attend this quiz & Test your knowledge.

Which one of the following is the same as 1.1?

Which of the following represents an ascending order of decimal numbers, which one of the following decimals is the smallest, choose the correct sign. 0.119 ____ 0.091.

What are terminating decimal numbers?

Terminating decimal numbers are numbers that have a finite number of digits after the decimal point, and they terminate after certain decimal places. For example, 0.5, 1.2345, etc.

What is the significance of ordering?

Ordering is an important part of life. Without ordering, analysis of sufficiently large data is almost impossible. We see ordering in almost every part of our life, like the order of events in a party, the order of items on a shelf, etc.

What are rational numbers in terms of decimals?

Rational numbers are numbers that have either terminating or non-terminating repeating decimal forms. These numbers can be represented as a fraction where the denominator is non-zero.

What are decimal fractions?

Decimal fractions are fractions whose denominator is a power of 10.

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Module 1A: Problem Solving and Proportional Reasoning

Learning outcomes.

  • Name a decimal number
  • Given the name of a decimal number, write it in decimal notation
  • Convert a decimal to a fraction or mixed number

You probably already know quite a bit about decimals based on your experience with money. Suppose you buy a sandwich and a bottle of water for lunch. If the sandwich costs [latex]\text{\$3.45}[/latex] , the bottle of water costs [latex]\text{\$1.25}[/latex] , and the total sales tax is [latex]\text{\$0.33}[/latex] , what is the total cost of your lunch?

A vertical addition problem is shown. The top line shows $3.45 for a sandwich, the next line shows $1.25 for water, and the last line shows $0.33 for tax. The total is shown to be $5.03.

Because [latex]\text{100 pennies}=\text{\$1}[/latex], each penny is worth [latex]{\Large\frac{1}{100}}[/latex] of a dollar. We write the value of one penny as [latex]$0.01[/latex], since [latex]0.01={\Large\frac{1}{100}}[/latex].

Writing a number with a decimal is known as decimal notation. It is a way of showing parts of a whole when the whole is a power of ten. In other words, decimals are another way of writing fractions whose denominators are powers of ten. Just as the counting numbers are based on powers of ten, decimals are based on powers of ten. The table below shows the counting numbers.

How are decimals related to fractions? The table below shows the relation.

When we name a whole number, the name corresponds to the place value based on the powers of ten. In Whole Numbers, we learned to read [latex]10,000[/latex] as ten thousand . Likewise, the names of the decimal places correspond to their fraction values. Notice how the place value names in the first table relate to the names of the fractions from the second table.

This chart illustrates place values to the left and right of the decimal point.

A chart is shown labeled

  • The “th” at the end of the name means the number is a fraction. “One thousand” is a number larger than one, but “one thousandth” is a number smaller than one.
  • The tenths place is the first place to the right of the decimal, but the tens place is two places to the left of the decimal.

Remember that [latex]$5.03[/latex] lunch? We read [latex]$5.03[/latex] as five dollars and three cents . Naming decimals (those that don’t represent money) is done in a similar way. We read the number [latex]5.03[/latex] as five and three hundredths . We sometimes need to translate a number written in decimal notation into words. As shown in the image below, we write the amount on a check in both words and numbers.

When we write a check, we write the amount as a decimal number as well as in words. The bank looks at the check to make sure both numbers match. This helps prevent errors.

An image of a check is shown. The check is made out to Jane Doe. It shows the number $152.65 and says in words,

The number [latex]15.68[/latex] is read fifteen and sixty-eight hundredths .

Name a decimal number.

  • Name the number to the left of the decimal point.
  • Write “and” for the decimal point.
  • Name the “number” part to the right of the decimal point as if it were a whole number.
  • Name the decimal place of the last digit.

Name each decimal:

1. [latex]4.3[/latex]

2. [latex]2.45[/latex]

3. [latex]0.009[/latex]

4. [latex]-15.571[/latex]

Now we will translate the name of a decimal number into decimal notation. We will reverse the procedure we just used.

1. Write the number six and seventeen hundredths:

2. Write fourteen and thirty-seven hundredths as a decimal.

In the following video we show more examples of how to write the name of a decimal using a place value chart.

Write a decimal number from its name.

  • Look for the word “and”—it locates the decimal point.
  • Place a decimal point under the word “and.” Translate the words before “and” into the whole number and place it to the left of the decimal point.
  • If there is no “and,” write a “0” with a decimal point to its right.
  • Translate the words after “and” into the number to the right of the decimal point. Write the number in the spaces—putting the final digit in the last place.
  • Fill in zeros for place holders as needed.

The second bullet in Step 1 is needed for decimals that have no whole number part, like ‘nine thousandths’. We recognize them by the words that indicate the place value after the decimal – such as ‘tenths’ or ‘hundredths.’ Since there is no whole number, there is no ‘and.’ We start by placing a zero to the left of the decimal and continue by filling in the numbers to the right, as we did above.

Write twenty-four thousandths as a decimal.

In the next video we will show more examples of how to write a decimal given its name in words.

Before we move on to our next objective, think about money again. We know that [latex]$1[/latex] is the same as [latex]$1.00[/latex]. The way we write [latex]$1\left(\text{or}$1.00\right)[/latex] depends on the context. In the same way, integers can be written as decimals with as many zeros as needed to the right of the decimal.

[latex]\begin{array}{cccc}5=5.0\hfill & & & -2=-2.0\hfill \\ 5=5.00\hfill & & & -2=-2.00\hfill \\ 5=5.000\hfill & & & -2=-2.000\hfill \end{array}[/latex] and so on [latex]\dots[/latex]

Converting decimals to fractions or mixed numbers

We often need to rewrite decimals as fractions or mixed numbers. Let’s go back to our lunch order to see how we can convert decimal numbers to fractions. We know that [latex]$5.03[/latex] means [latex]5[/latex] dollars and [latex]3[/latex] cents. Since there are [latex]100[/latex] cents in one dollar, [latex]3[/latex] cents means [latex]{\Large\frac{3}{100}}[/latex] of a dollar, so [latex]0.03={\Large\frac{3}{100}}[/latex].

We convert decimals to fractions by identifying the place value of the farthest right digit. In the decimal [latex]0.03[/latex], the [latex]3[/latex] is in the hundredths place, so [latex]100[/latex] is the denominator of the fraction equivalent to [latex]0.03[/latex].

[latex]0.03={\Large\frac{3}{100}}[/latex]

For our [latex]$5.03[/latex] lunch, we can write the decimal [latex]5.03[/latex] as a mixed number.

[latex]5.03=5{\Large\frac{3}{100}}[/latex]

Notice that when the number to the left of the decimal is zero, we get a proper fraction. When the number to the left of the decimal is not zero, we get a mixed number.

Convert a decimal number to a fraction or mixed number.

  • If it is zero, the decimal converts to a proper fraction.
  • Write the whole number.
  • Determine the place value of the final digit.
  • numerator—the ‘numbers’ to the right of the decimal point
  • denominator—the place value corresponding to the final digit
  • Simplify the fraction, if possible.

Write each of the following decimal numbers as a fraction or a mixed number:

  • [latex]4.09[/latex]
  • [latex]3.7[/latex]
  • [latex]-0.286[/latex]

Did you notice that the number of zeros in the denominator is the same as the number of decimal places?

In the next video example, we who how to convert a decimal into a fraction.

Locating and ordering decimals with a number line

Since decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line.

Locate [latex]0.4[/latex] on a number line.

Solution The decimal [latex]0.4[/latex] is equivalent to [latex]{\Large\frac{4}{10}}[/latex], so [latex]0.4[/latex] is located between [latex]0[/latex] and [latex]1[/latex]. On a number line, divide the interval between [latex]0[/latex] and [latex]1[/latex] into [latex]10[/latex] equal parts and place marks to separate the parts.

Label the marks [latex]0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0[/latex]. We write [latex]0[/latex] as [latex]0.0[/latex] and [latex]1[/latex] as [latex]1.0[/latex], so that the numbers are consistently in tenths. Finally, mark [latex]0.4[/latex] on the number line.

A number line is shown with 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 labeled. There is a red dot at 0.4.

Locate [latex]-0.74[/latex] on a number line.

Solution The decimal [latex]-0.74[/latex] is equivalent to [latex]-{\Large\frac{74}{100}}[/latex], so it is located between [latex]0[/latex] and [latex]-1[/latex]. On a number line, mark off and label the multiples of [latex]-0.10[/latex] in the interval between [latex]0[/latex] and [latex]-1[/latex] ( [latex]-0.10[/latex] , [latex]-0.20[/latex] , etc.) and mark [latex]-0.74[/latex] between [latex]-0.70[/latex] and [latex]-0.80[/latex], a little closer to [latex]-0.70[/latex] .

A number line is shown with negative 1.00, negative 0.90, negative 0.80, negative 0.70, negative 0.60, negative 0.50, negative 0.40, negative 0.30, negative 0.20, negative 0.10, and 0.00 labeled. There is a red dot between negative 0.80 and negative 0.70 labeled as negative 0.74.

In the next video we show more examples of how to locate a decimal on the number line.

Order Decimals

Which is larger, [latex]0.04[/latex] or [latex]0.40?[/latex]

If you think of this as money, you know that [latex]$0.40[/latex] (forty cents) is greater than [latex]$0.04[/latex] (four cents). So,

[latex]0.40>0.04[/latex]

In previous chapters, we used the number line to order numbers.

[latex]\begin{array}{}\\ a<b\text{ , }a\text{ is less than }b\text{ when }a\text{ is to the left of }b\text{ on the number line}\hfill \\ a>b\text{ , }a\text{ is greater than }b\text{ when }a\text{ is to the right of }b\text{ on the number line}\hfill \end{array}[/latex]

Where are [latex]0.04[/latex] and [latex]0.40[/latex] located on the number line?

A number line is shown with 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 labeled. There is a red dot between 0.0 and 0.1 labeled as 0.04. There is another red dot at 0.4.

How does [latex]0.31[/latex] compare to [latex]0.308?[/latex] This doesn’t translate into money to make the comparison easy. But if we convert [latex]0.31[/latex] and [latex]0.308[/latex] to fractions, we can tell which is larger.

Because [latex]310>308[/latex], we know that [latex]{\Large\frac{310}{1000}}>{\Large\frac{308}{1000}}[/latex]. Therefore, [latex]0.31>0.308[/latex].

Notice what we did in converting [latex]0.31[/latex] to a fraction—we started with the fraction [latex]\Large\frac{31}{100}[/latex] and ended with the equivalent fraction [latex]\Large\frac{310}{1000}[/latex]. Converting [latex]\Large\frac{310}{1000}[/latex] back to a decimal gives [latex]0.310[/latex]. So [latex]0.31[/latex] is equivalent to [latex]0.310[/latex]. Writing zeros at the end of a decimal does not change its value.

[latex]{\Large\frac{31}{100}}={\Large\frac{310}{1000}}\text{ and }0.31=0.310[/latex]

If two decimals have the same value, they are said to be equivalent decimals.

[latex]0.31=0.310[/latex]

We say [latex]0.31[/latex] and [latex]0.310[/latex] are equivalent decimals.

Equivalent Decimals

Two decimals are equivalent decimals if they convert to equivalent fractions.

Remember, writing zeros at the end of a decimal does not change its value.

Order decimals

  • Check to see if both numbers have the same number of decimal places. If not, write zeros at the end of the one with fewer digits to make them match.
  • Compare the numbers to the right of the decimal point as if they were whole numbers.
  • Order the numbers using the appropriate inequality sign.

Order the following decimals using [latex]<\text{ or }\text{>}[/latex]:

  • [latex]0.64[/latex] ____ [latex]0.6[/latex]
  • [latex]0.83[/latex] ____ [latex]0.803[/latex]

When we order negative decimals, it is important to remember how to order negative integers. Recall that larger numbers are to the right on the number line. For example, because [latex]-2[/latex] lies to the right of [latex]-3[/latex] on the number line, we know that [latex]-2>-3[/latex]. Similarly, smaller numbers lie to the left on the number line. For example, because [latex]-9[/latex] lies to the left of [latex]-6[/latex] on the number line, we know that [latex]-9<-6[/latex].

A number line is shown with integers from negative 10 to 0. Blue dots are placed on negative nine and negative six. Red dots are placed at negative two and negative three.

Use [latex]<\text{or}>[/latex]; to order. [latex]-0.1[/latex] ____ [latex]- 0.8[/latex].

In the following video lesson we show how to order decimals using inequality notation by comparing place values, and by using fractions.

Rounding decimals

In the United States, gasoline prices are usually written with the decimal part as thousandths of a dollar. For example, a gas station might post the price of unleaded gas at [latex]\$3.279[/latex] per gallon. But if you were to buy exactly one gallon of gas at this price, you would pay [latex]$3.28[/latex] , because the final price would be rounded to the nearest cent. In a lesson about whole numbers, we learned that we can round numbers to get an approximate value when the exact value is not needed.

Suppose we wanted to round [latex]$2.72[/latex] to the nearest dollar. Is it closer to [latex]$2[/latex] or to [latex]$3[/latex]? What if we wanted to round [latex]$2.72[/latex] to the nearest ten cents; is it closer to [latex]$2.70[/latex] or to [latex]$2.80[/latex]? The number lines in the image below can help us answer those questions.

(a) We see that [latex]2.72[/latex] is closer to [latex]3[/latex] than to [latex]2[/latex]. So, [latex]2.72[/latex] rounded to the nearest whole number is [latex]3[/latex].

(b) We see that [latex]2.72[/latex] is closer to [latex]2.70[/latex] than [latex]2.80[/latex]. So we say that [latex]2.72[/latex] rounded to the nearest tenth is [latex]2.7[/latex].

In part a, a number line is shown with 2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 and 3. There is a dot between 2.7 and 2.8 labeled as 2.72. In part b, a number line is shown with 2.70, 2.71, 2.72, 2.73, 2.74, 2.75, 2.76, 2.77, 2.78, 2.79, and 2.80. There is a dot at 2.72.

Round a decimal.

  • Locate the given place value and mark it with an arrow.
  • Underline the digit to the right of the given place value.
  • Yes – add [latex]1[/latex] to the digit in the given place value.
  • No – do not change the digit in the given place value
  • Rewrite the number, removing all digits to the right of the given place value.

Tip For Success

If the digit to the right of your given place value is 5 or above, give your given place value a shove.

If the digit to the right of your given place value is 4 or less, let your given place value rest.

Round [latex]18.379[/latex] to the nearest hundredth.

Round [latex]18.379[/latex] to the nearest

  • whole number Show Solution

Watch the following video to see an example of how to round a number to several different place values.

  • Question ID 146571, 146572, 146568,146569, 146224, 146225. Authored by : Lumen Learning. License : CC BY: Attribution
  • Question ID 146574, 146575, 146576. Authored by : Lumen Learning. License : CC BY: Attribution
  • Question ID 146237, 146238, 146239. Authored by : Lumen Learning. License : CC BY: Attribution
  • Question ID 146239, 146242, 146244. Authored by : Lumen Learning. License : CC BY: Attribution . License Terms : IMathAS Community License CC-BY + GPL
  • Read and Write Decimals. Authored by : James Sousa (Mathispower4u.com). Located at : https://youtu.be/aLsWWl2-aNE . License : CC BY: Attribution
  • Examples: Write a Number in Decimal Notation from Words. Authored by : James Sousa (Mathispower4u.com). Located at : https://youtu.be/d1_1q1Dj1zY . License : CC BY: Attribution
  • Ex 1: Convert a Decimal to a Fraction. Authored by : James Sousa (Mathispower4u.com). Located at : https://youtu.be/0yYQLZcTEXc . License : CC BY: Attribution
  • Example: Identify Decimals on the Number Line. Authored by : James Sousa (Mathispower4u.com). Located at : https://youtu.be/F3LAKsOBdNA . License : CC BY: Attribution
  • Decimal Notation: Ordering Decimals. Authored by : James Sousa (Mathispower4u.com). Located at : https://youtu.be/fjO3fnt3ABA . License : CC BY: Attribution
  • Examples: Rounding Decimals. Authored by : James Sousa (Mathispower4u.com). Located at : https://youtu.be/qu4Y9DGqXlk . License : CC BY: Attribution
  • Prealgebra. Provided by : OpenStax. License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

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Ordering Decimals - Grid Puzzles

Ordering Decimals - Grid Puzzles

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Mr. Thompson's Shop

Last updated

16 September 2022

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ordering decimals reasoning and problem solving

A Bronze/Silver/Gold differentiated resource where pupils are given a list of decimals and a square grid. Pupils have to put the decimals into the grid so that each row and column is in ascending order.

In Bronze, the integer part of each decimal is the same. In Silver, the integer parts are different. In Gold, negatives are introduced. The grids get progressively larger as you move from Bronze to Gold as well.

Each puzzle has multiple solutions, but I’ve provided one possible solution to each.

Update 16/9/22: Changed the design of the tasks, but the content is the same.

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  • Tuesday - Order and Compare Decimals
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  • Lesson-2-Y5-Spring-Block-3-WO7-Order-and-compare-decimals-2019.pdf
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Varied Fluency - if you want to develop your understanding of decimals up to 2 decimal places further, have a go at this task. Remember to choose Hot (D), Fiery (E) or Extreme (GD). Scroll down to page 5 for the answers.

  • Year-5-Spring-Block-3-Step-7-VF-Order-and-Compare-Decimals.pdf

Reasoning - have a go at applying your knowledge. Remember to choose Hot (D), Fiery (E) or Extreme (GD).

  • Year-5-Spring-Block-3-Step-7-RPS-Order-and-Compare-Decimals.pdf

Unfortunately not the ones with chocolate chips.

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ordering decimals reasoning and problem solving

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Round Decimals – Reasoning and Problem Solving

Round Decimals - Reasoning and Problem Solving

Round Decimals - Reasoning and Problem Solving

This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of rounding decimals.

ordering decimals reasoning and problem solving

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What's included in the pack? Round Decimals Reasoning and Problem Solving worksheet Answer sheet

National Curriculum Objectives:

  • (6F10)  Solve problems which require answers to be rounded to specified degrees of accuracy

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ordering decimals reasoning and problem solving

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ordering decimals reasoning and problem solving

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IMAGES

  1. Order decimals

    ordering decimals reasoning and problem solving

  2. ordering decimals problem solving year 4

    ordering decimals reasoning and problem solving

  3. Mastery in maths year 5 Read, write order and compare decimals fluency

    ordering decimals reasoning and problem solving

  4. Round Decimals

    ordering decimals reasoning and problem solving

  5. ordering decimals problem solving year 4

    ordering decimals reasoning and problem solving

  6. ordering decimals problem solving year 4

    ordering decimals reasoning and problem solving

VIDEO

  1. GCSE 9-1 Mathematics Key Topic: Ordering Decimals

  2. Art of Problem Solving: Adding Decimals

  3. Rounding of Decimal Numbers (Mathematics Fourth Grade)

  4. order of operations with fractions and decimals‬‏

  5. Place Value

  6. ORDER FRACTIONS AND DECIMALS| GED BASIC MATH

COMMENTS

  1. PDF Year 4 Order Decimals Reasoning and Problem Solving

    Reasoning and Problem Solving Order Decimals Reasoning and Problem Solving Order Decimals Developing 1a. There are 4 possible answers: 0.74, 0.42, 0.72, 0.47 2a. Billie is partly correct because 0.22 is greater than 0.14 but 0.14 is not greater than 0.24 as 0.24 has 1 more tenth than 0.14 and 2 more hundredths than 0.22. 3a.

  2. PDF Year 5 Order and Compare Decimals Reasoning and Problem Solving

    Reasoning and Problem Solving - Order and Compare Decimals - Teaching Information. 1a.Oliver made a number between two and three tenths and 2.85 using counters on a place value mat. Oliver's number. D. 1b. Jamie made a number between 3.22 and 3.95 using counters on a place value chart. Five of the counters have fallen off.

  3. PDF Year 5 Decimals up to 2dp Reasoning and Problem Solving

    Reasoning and Problem Solving Decimals up to 2d.p. Reasoning and Problem Solving Decimals up to 2d.p. Developing 1a. D is the odd one out as it represents 7.42. The others represent 7.24. 2a. 8.36 3a. Matt is incorrect as he has made 3.47 instead of 4.73. Expected 4a. A is the odd one out as it represents 5.3. The others represent 4.13.

  4. Ordering Decimals: Definition, Types, Steps, Examples, Facts

    Step 1: Use the place value chart! Write the decimals in the place value chart such that the place values of all the decimals are aligned. The empty boxes at the end of the decimal can be filled with zeroes. Step 2: Compare the whole number part first. Always start comparing the digits at the highest place value.

  5. PDF Year 5 Decimal Sequences Reasoning and Problem Solving

    Reasoning and Problem Solving - Decimal Sequences - Year 5 Developing. 4a. 0.763 0.7 0.637 0.574 0.511. 0.5 will be a term in this sequence. Emily Adam The sequence is reducing by 0.63 with each term. E. 4b. 7.98 6.99 6 5.01 4.02. Our next term will be a smaller number than we have now.

  6. Decimals

    Order decimals. Check to see if both numbers have the same number of decimal places. If not, write zeros at the end of the one with fewer digits to make them match. Compare the numbers to the right of the decimal point as if they were whole numbers. Order the numbers using the appropriate inequality sign.

  7. Year 4 Order Decimals Lesson

    This Year 4 Order Decimals lesson covers the prior learning of hundredths on a place value chart and comparing decimals, before moving onto the main skill of ordering decimals. ... This powerpoint can be used to model the questions that the children will complete on the Varied Fluency and Reasoning & Problem Solving worksheets as part of this ...

  8. White Rose Maths Compatible Ordering Decimals Year 4 Mastery

    A mastery-style pack which helps children to deepen their understanding of ordering decimals at year 4 level: an ideal resource to reinforce their knowledge. ... The pack includes worksheets with fluency, reasoning, and problem-solving activities, as well as a PowerPoint which helps model some of the questions included in the worksheets.

  9. PDF Year 5 Thousandths as Decimals Reasoning and Problem Solving

    Reasoning and Problem Solving - Thousandths as Decimals - Year 5 Developing. 4a.Max and Isaac are expanding 2.491. 4b. Millie and Flo are expanding 9.529. 5a.Hafsa is thinking of a number. It has 5 ones. It has 2 tenths and 0 hundredths. It has an unknown amount of thousandths. 5b.

  10. PDF Year 6 Three Decimal Places Reasoning and Problem Solving

    Reasoning and Problem Solving Three Decimal Places Reasoning and Problem Solving Three Decimal Places Developing 1a. One box is empty as none of the numbers are greater than 2.5 with a value greater than 2 in the hundredths column. 2a. Various answers, for example: 4.61, 4.71, 4.81, 4.91, 5.01 3a. B: 5.52; the others describe 5.25. Expected 4a.

  11. Decimals Reasoning and Problem Solving

    Decimals Reasoning and Problem Solving. Subject: Mathematics. Age range: 7-11. Resource type: Worksheet/Activity. File previews. pdf, 394.64 KB. These problems will give your Year 6 pupils the opportunity to reason and solve problems with decimals. This is a sample resource. For a full year's worth of reasoning and problem solving for Year 6 ...

  12. PDF Year 5 Rounding Decimals Reasoning and Problem Solving

    Reasoning and Problem Solving Step 6: Rounding Decimals. National Curriculum Objectives: Mathematics Year 5: (5F7) Round decimals with two decimal places to the nearest whole number and to one decimal place. Differentiation: Questions 1, 4 and 7 (Problem Solving) Developing Complete the maze by travelling through decimal numbers (up to 1 ...

  13. PDF Year 5 Understand Thousandths Reasoning and Problem Solving

    Reasoning and Problem Solving Understand Thousandths Reasoning and Problem Solving Understand Thousandths Developing 1a. is the odd one out because its matching decimal 0.637 is not given. 2a. Various possible answers, for example: 0.549 = , 0.459 = , 0.945 = 3a. A -Luke, B -Sasha Expected 4a. 0.45 is the odd one out because its

  14. Y5 DiM: Step 9 Order and Compare Decimals to 3 Places Pack

    This comprehensive and visually engaging teaching resource supports the White Rose Maths Y5 small step 9: 'Order and Compare Any Decimals with up to 3 Decimal Places'. This teaching pack provides structured activities and a PowerPoint for mastery of this important concept. The PowerPoint presentation features a diverse range of useful activities to embed children's learning. Designed for both ...

  15. Ordering Decimals

    Ordering Decimals - Grid Puzzles. A Bronze/Silver/Gold differentiated resource where pupils are given a list of decimals and a square grid. Pupils have to put the decimals into the grid so that each row and column is in ascending order. In Bronze, the integer part of each decimal is the same. In Silver, the integer parts are different.

  16. PDF Year 3 Tenths as Decimals Reasoning and Problem Solving

    Reasoning and Problem Solving Tenths as Decimals Reasoning and Problem Solving Tenths as Decimals Developing 1a. Yes because he has used five counters to represent five tenths. 2a. C because it shows and the others are . 3a. 0.2, 0.4, 0.8, 0.9 Expected 4a. No because she has used eight straws instead of nine. 5a.

  17. Tuesday

    Varied Fluency - if you want to develop your understanding of decimals up to 2 decimal places further, have a go at this task. Remember to choose Hot (D), Fiery (E) or Extreme (GD). Scroll down to page 5 for the answers. Year-5-Spring-Block-3-Step-7-VF-Order-and-Compare-Decimals.pdf

  18. PDF Year 6 Fractions to Decimals 1 Reasoning and Problem Solving

    Expected Convert fractions to decimals and order correctly when converting common fractions and fractions where the denominator is a multiple or factor of 10. Greater Depth Convert fractions to decimals and order correctly when using knowledge of common fractions for example 1/4 = 0.25 therefore 1/8 = 0.125. Questions 3, 6 and 9 (Problem Solving)

  19. PDF Year 5 Percentages as Fractions and Decimals Reasoning and Problem Solving

    Reasoning and Problem Solving Percentages as Fractions and Decimals Reasoning and Problem Solving Percentages as Fractions and Decimals Developing 1a. Year 5 have 20 glue sticks, Year 3 have 40 glue sticks. There are 40 glue sticks left which is 40%. 2a. 48%, 47%, 45%, 40%, 4% 3a. Alice is correct = 5%. Johnny is incorrect, 0.05 = 5% not 50% ...

  20. Round Decimals

    This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of rounding decimals. MENU MENU. ... Unit 7 Ordering Food Lesson; Unit 8 Dates and Times Lesson; ... Round Decimals Reasoning and Problem Solving worksheet