Ordering Decimals

In ordering decimals we will learn how to compare two or more decimals.

(i) Convert each of them as like decimals.

(ii) Compare these decimals just as we compare two whole numbers ignoring decimal point.

1. Which is greater of 0.89 and 2.01?

Since whole number part 2 > whole number part 0

Therefore, 2.01 > 0.89

2. Arrange in increasing order: 4.91, 13.01, 12.1, 18.123, 13.9, 4.53

Largest decimal places are in 18.123 that is 3

Therefore, convert each of the decimal number into like decimals with 3 decimal places.

4.91 = 4.910                        ....... 2

13.01 = 13.010                    ....... 4

12.1 = 12.100                      ....... 3

18.123 = 18.123                  ....... 6

13.9 = 13.900                      ....... 5

4.53 = 4.530                        ....... 1

4.53, 4.91, 12.1, 13.01, 13.9, 18.123

3. Write the decimal numbers in ascending order using < sign:

(i) 4.926, 18.324, 18.428, 18.528, 18.234

The given decimal numbers are like decimals with 3 decimal places.

To arrange the decimal numbers in ascending order, first check the whole number part of all the decimal numbers. We see 4 is the smallest whole number part so, 4.926 is the smallest decimal number.

The rest of the decimal numbers have the same whole number part i.e. 18. Now we will compare the decimal part of 18.324, 18.428, 18.528 and 18.234 just as we compare the whole numbers ignoring the decimal points.

Clearly, we see 234 < 324 < 428 < 528

i.e. 18.234 < 18.324 < 18.428 < 18.528

Therefore, 4.926 < 18.234 < 18.324 < 18.428 < 18.528

(ii) 72.09, 72.19, 72.91, 72.17, 72.81

The given decimal numbers are like decimals with 2 decimal places and they have the same whole number part i.e. 72.

Now we will compare the decimal part of 72.09, 72.19, 72.91, 72.17 and 72.81 just as we compare the whole numbers ignoring the decimal points.

Clearly, we see 09 < 17 < 19 < 81 < 91

Therefore, 72.09 < 72.17 < 72.19 < 72.81 < 72.91

(iii) 301.13, 301.03, 301.31, 301.30

Since the whole number part of all the decimal numbers are same here we need to compare the decimal part just as we compare the whole numbers ignoring the decimal points.

301.13, 301.03, 301.31, 301.30

Clearly, we see 03 < 13 < 30 < 31

Therefore, 301.03 < 301.13 < 301.30 < 301.31


(iv) 107.08, 107.81, 107.80, 107.88

These decimal numbers are like decimals with the same whole number part so we compare these decimals just as we compare the whole numbers ignoring decimal point.

107.08, 107.81, 107.80, 107.88

Clearly, we see 08 < 80 < 81 < 88

Therefore, 107.08 < 107.80 < 107.81 < 107.88

4. Arrange 32.21, 2.324, 14.73, 6.4 in ascending order.

Solution:

On converting the decimal fractions into like decimals, we get

32.210, 2.324, 14.730,6.400

Now, 2.324 is the smallest decimal. The next decimal greater than 2.324 is 6.400. The other decimals in ascending order are: 14.730, 32.210.

Then, the given decimals in ascending order are:

2.324, 6.400, 14.730, 32.210, i.e., 2.324, 6.4, 14.73, 32.21.

5. Arrange 2.49, 7.16, 23.5, 5.35 in descending order.

Solution:

The greatest decimal is 23.5. The next decimal smaller than 23.5 is 7.16. The other decimals in descending order are 5.35 and 2.49.

Hence, the given decimals in descending order are:

23.5, 7.16, 5.35, 2.49.

Worksheet on Comparing and Ordering Decimals:

1. Compare the following pairs of decimals:

(i) 8.27 and 3.26

(ii) 5.312 and 5.407

(iii) 3.21 and 0.513

(iv) 35.146053 and 1.067

(v) 23.07 and 21.156

(vi) 0.467 and 0.87

Answer:

1. (i) 8.27 > 3.26

(ii) 5.312 < 5.407

(iii) 3.21 > 0.513

(iv) 35.146053 > 1.067

(v) 23.07 > 21.156

(vi) 0.467 < 0.87

2. Arrange the following decimals in descending order:

(i) 6.6, 23.94, 7.96, 35.275

(ii) 12.05, 42.14, 16.50, 8.69

(iii) 36.75, 58.5, 48.6, 9.7

(iv) 86.351, 205.25, 346.87, 87.4

Answer:

2. (i) 35.275, 23.94, 7.96, 6.6

(ii) 42.14, 16.50, 12.05, 8.69

(iii) 58.5, 48.6, 36.75, 9.7

(iv) 346.87, 205.25, 87.4, 86.351

3. Arrange the following decimals in ascending order:

(i) 26.5, 5.07, 82.008, 23.4

(ii) 27.6, 24.63, 39.532, 76.943

(ⅲ) 47.6, 31.085, 37.54, 142.514

(iv) 0.33, 0.3, 3.03, 3.033

Answer:

3. (i) 5.07, 23.4, 26.5, 82.008

(ii) 24.63, 27.6, 39.532, 76.943

(iii) 31.085, 37.54, 47.6, 142.514

(iv) 0.3, 0.33, 3.03, 3.033

● Decimal.

Decimal Place Value Chart.

Expanded form of Decimal Fractions.

Like Decimal Fractions.

Unlike Decimal Fraction.

Equivalent Decimal Fractions.

Changing Unlike to Like Decimal Fractions.

Ordering Decimals

Comparison of Decimal Fractions.

Conversion of a Decimal Fraction into a Fractional Number.

Conversion of Fractions to Decimals Numbers.

Addition of Decimal Fractions.

Problems on Addition of Decimal Fractions

Subtraction of Decimal Fractions.

Problems on Subtraction of Decimal Fractions

Multiplication of a Decimal Numbers.

Multiplication of a Decimal by a Decimal.

Properties of Multiplication of Decimal Numbers.

Problems on Multiplication of Decimal Fractions

Division of a Decimal by a Whole Number.

Division of Decimal Fractions

Division of Decimal Fractions by Multiples.

Division of a Decimal by a Decimal.

Division of a whole number by a Decimal.

Properties of Division of Decimal Numbers

Problems on Division of Decimal Fractions

Conversion of fraction to Decimal Fraction.

Simplification in Decimals.

Word Problems on Decimal.

5th Grade Numbers Page

5th Grade Math Problems

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