Expanded form of Decimal Fractions

We will discuss here about the expanded form of decimal fractions.

In expanded form of decimal fractions we will learn how to read and write the decimal numbers.

Decimal numbers can be expressed in expanded form using the place-value chart. Let us consider the number 561.129. Let us expand each of the digits using the place-value chart.

So, we can write 561.129 in the expanded form as follows.

561.129 = 500 + 60 + 1 + 0.1 + 0.02 + 0.009

             = 5 hundreds + 6 tens + 1 ones + 1 tenths + 2 hundredths + 9 thousandths

             = 500 + 60 + 1 + $\frac{1}{10}$ + $\frac{2}{100}$ + $\frac{9}{1000}$

Again,

493.2 = 4 hundreds + 9 tens + 3 ones + 2 tenths

         = 400 + 90 + 3 + $\frac{2}{10}$

1436.74 = 1 thousands + 4 hundreds + 3 tens + 6 ones + 7 tenths + 4 hundredths

             = 1000 + 400 + 30 + 6 + $\frac{7}{10}$ + $\frac{4}{100}$

Note: When a decimal is missing either in the integral part or decimal part, substitute with 0. 

Consider the number 123.437

Let us write the digits if this number as per their place value.

123.437 = 1 hundreds + 2 tens + 3 ones + 4 tenths + 3 hundredths + 7 thousandths

             = 100 + 20 + 3 + 4/10 + 3/100 + 7/1000

             = 100 + 20 + 3 + 0.4 + 0.03 + 0.007

Thus, 123.437 = 100 + 20 + 3 + 0.4 + 0.03 + 0.007

1. Write the decimal numbers in expanded form:

(i) 3479.105

= 3 thousands + 4 hundreds + 7 tens + 9 ones + 1 tenths + 0 hundredths+ 5 thousandths

= 3000 + 400 + 70 + 9 + $\frac{1}{10}$ + $\frac{0}{100}$ + $\frac{5}{1000}$

(ii) 7833.45

= 7 thousands + 8 hundreds + 3 tens + 3 ones + 4 tenths + 5 hundredths

= 7000 + 800 + 30 + 3 + $\frac{4}{10}$ + $\frac{5}{100}$

(iii) 21.1097

= 2 tens + 1 ones + 1 tenths + 0 hundredths + 9 thousandths + 7 ten thousandths

= 20 + 1 + $\frac{1}{10}$ + $\frac{0}{100}$ + $\frac{9}{1000}$ + $\frac{7}{10000}$

(iv) 524.1

= 5 hundreds + 2 tens + 4 ones + 1 tenths

= 500 + 20 + 4 + $\frac{1}{10}$

(v) 143.011

= 1 hundreds + 4 tens + 3 ones + 0 tenths + 1 hundredths + 1 thousandths

= 100 + 40 + 3 + $\frac{0}{10}$ + $\frac{1}{100}$ + $\frac{1}{1000}$

(vi) 840.006

= 8 hundreds + 4 tens + 0 ones + 0 tenths + 0 hundredths + 6 thousandths

= 800 + 40 + 0 + $\frac{0}{10}$ + $\frac{0}{100}$ + $\frac{6}{1000}$

(vii) 64.21

= 6 tens + 4 ones + 2 tenths + 1 hundredths

= 60 + 4 + $\frac{2}{10}$ + $\frac{1}{100}$

(viii) 4334.334

= 4 thousands + 3 hundreds + 3 tens + 4 ones + 3 tenths + 3 hundredths + 4 thousandths

= 4000 + 300 + 30 + 4 + $\frac{3}{10}$ + $\frac{3}{100}$ + $\frac{4}{1000}$

2. Write as decimal fractions:

(i) 8 thousands + 8 ones + 3 tenths + 9 hundredths

= 8008.39

(ii) 4000 + 7 + $\frac{5}{10}$ + $\frac{6}{100}$

= 4007.56

(iii) 6 hundreds + 9 tens + 8 tenths + 4 thousandths

= 690.804

(iv) 3 tens + 7 ones + 6 hundredths + 8 thousandths

= 37.068

(v) 400 + 50 + 1 + $\frac{9}{100}$

= 451.09

(vi) 800 + 70 + 2 + $\frac{8}{10}$ + $\frac{5}{1000}$

= 872.805

(vii) 6 tens + 5 tenths + 8 hundredths

= 60.58

(viii) 9 hundreds + 4 tens + 3 tenths + 4 hundredths

= 940.34

3. Write the following in short form.

(i) 100 + 0.5 + 0.06 + 0.008             (ii) 80 + 1 + 0.02 + 0.005

Solution:

(i) 100 + 0.5 + 0.06 + 0.008           

= 100.568            

(ii) 80 + 1 + 0.02 + 0.005

= 81.025

4. Write the place-value of the underlined digits.

(i) 2.47                                (ii) 11.003                           (iii) 5.175

Solution:

(i) 2.47 

Place-value of 7 in 2.47 is 7 hundredths or 0.07.

(ii) 11.003

Place-value of 3 in 11.003 is 3 thousandths or 0.003.

(iii) 5.175

Place-value of 1 in 5.175 is 1 tenths or 0.1.

Expanded form of Decimals:

This is a form in which we add the place value of each digit forming the number.

Practice Problems on Expanded Form of Decimal Fractions:

I. Write each of the following decimals in expanded form:

(i) 38.54

(ii) 83.107

(iii) 627.074

Solution:

(i) 38.54 = 38 + $\frac{5}{10}$ + $\frac{4}{100}$ = 30 + 8 + 0.5 + 0.04

(ii) 83.107 = 83 + $\frac{1}{10}$ + $\frac{0}{100}$ + $\frac{7}{1000}$

                = 80 + 3 + 0.1 + 0 + 0.007

                = 80 + 3 + 0.1 + 0.007

(ii) 627.074 = 627 + $\frac{0}{10}$ + $\frac{7}{100}$ + $\frac{4}{1000}$

                  = 600 + 20 + 7 + 0 + 0.07 + 0.004

                  = 600 + 20 + 7 + 0.07 + 0.004

II. Write following in short form:

(i) 9 + $\frac{3}{10}$ + $\frac{4}{100}$

(ii) 50 + 7 + $\frac{6}{10}$ + $\frac{2}{100}$ + $\frac{4}{1000}$

(iii) 100 + 4 + $\frac{3}{10}$ + $\frac{6}{1000}$

Solution:

(i) 9 + $\frac{3}{10}$ + $\frac{4}{100}$ = 9.34

(ⅱ) 50 + 7 + $\frac{6}{10}$ + $\frac{2}{100}$ + $\frac{4}{1000}$ = 57.624

(iii) 100 + 4 + $\frac{3}{10}$ + $\frac{6}{1000}$ = 104.306

Worksheet on Expanded form of Decimal Fractions

I. Write the given decimals in expanded form by fractional expansion.

One example has been done for you to get the idea how to do decimals in expanded form by fractional expansion.

1.73 = 1 + $\frac{7}{10}$ + $\frac{3}{100}$

(i) 23.8

(ii) 60.27

(iii) 119.05

(iv) 276.207

Answers:

I. (i) 20 + 3 + $\frac{8}{10}$

(ii) 60 + 0 + $\frac{2}{10}$ + $\frac{7}{100}$

(iii) 100 + 10 + 9 + 0 + $\frac{5}{100}$

(iv) 200 + 70 + 6 + $\frac{2}{10}$ + 0 + $\frac{7}{100}$

II. Write the given decimals in expanded form by decimal expansion.

One example has been done for you to get the idea how to do decimals in expanded form by decimal expansion.

8.461 = 8 + 0.4 + 0.06 + 0.001

(i) 6.08

(ii) 36.505

(iii) 402.613

(iv) 700.037

Answers:

II. (i) 6 + 0.0 + 0.08

(ii) 30 + 6 + 0.5 + 0.00 + 0.005

(iii) 400 + 0 + 2 + 0.6 + 0.01 + 0.003

(iv) 700 + 0 + 0 + 0.0 + 0.03 + 0.007

III. Write the decimal number for the expansions given below.

(i) 10 + 6 + $\frac{3}{10}$ + $\frac{9}{1000}$

(ii) 600 + 20 + 7 + $\frac{1}{10}$ + $\frac{3}{100}$ + $\frac{7}{1000}$

(iii) 2000 + 8 + $\frac{3}{10}$ + $\frac{9}{100}$

(iv) 400 + 70 + 1 + 0.5 + 0.07 + 0.002

(v) 5000 + 80 + 0 + 0.2 + 0.002

Answers:

III. (i) 16.309

(ii) 627.137

(iii) 2008.39

(iv) 471.572

(v) 5080.202

IV. Write the following decimals in expanded form:

(i) 31.5

(ii) 37.53

(iii) 307.85

(iv) 752.34

(ν) 882.146

(vi) 41.005

(vii) 345.083

(viii) 435.202

Answer:

IV. (i) 31.5 = 31 + 05

(ii) 37.53 = 30 + 7 + 0.5 + 0.03

(iii) 307.85 = 300 + 7 + 0.8 + 0.05

(iv) 752.34 = 700 + 50 + 2 + 0.3 + 0.04

(ν) 882.146 = 800 + 80 + 2 + 0.1 + 0.04 + 0.006

(vi) 41.005 = 40 + 1 + 0.005

(vii) 345.083 = 300 + 40 + 5 + 0.08 + 0.003

(viii) 435.202 = 400 + 30 + 5 + 0.2 + 0.002

V. Write each of the following in decimal form:

(i) 9 + 4/10 + 6/100 + 2/1000

(ii) 600 + 40 + 5/1000

(iii) 300 + 3 + 5/10 + 2/1000

(iv) 700 + 40 + 7 + 2/100 + 3/1000

Answer:

V. (i) 9.462

(ii) 640.005

(iii) 303. 502

(iv) 747.023 

VI. Fill in the boxes with correct numbers:

(i) 84.29 = 80 + 🔲 + $\frac{2}{10}$+ $\frac{9}{🔲}$

(ii) 35.265= 30 + 5 + $\frac{🔲}{10}$ + $\frac{6}{100}$ + $\frac{5}{🔲}$

(iii) 5672.053= 5000 + 600 + 🔲 + 🔲 + $\frac{5}{🔲}$ + $\frac{3}{🔲}$

Answer:

VI. (i) 84.29 = 80 + 4 + $\frac{2}{10}$ + $\frac{9}{\mathbf{{\color{Red}100}}}$

(ii) 35.265= 30 + 5 + $\frac{\mathbf{{\color{Red}2}}}{10}$ + $\frac{6}{100}$ + $\frac{5}{\mathbf{{\color{Red}1000}}}$

(iii) 5672.053= 5000 + 600 + 70 + 2 + $\frac{5}{\mathbf{{\color{Red}100}}}$ +  $\frac{3}{\mathbf{{\color{Red}1000}}}$

VII. Express in expanded form.

(i) 4.326

(ii) 29.629

(iii) 62.346

(iv) 28.429

(v) 82.031

(vi) 29.079

(vii) 97.458

(viii) 49.309

(ix) 318.073

(x) 518.318

(xi) 327.209

(xii) 214.342

(xiii) 617.829

(xiv) 970.079

(xv) 214.342

(xvi) 652.493

Answer:

VII. (i) 4 + 0.3 + 0.02 + 0.006

(ii) 20 + 9 + 0.6 + 0.02 + 0.009

(iii) 60 + 2 + 0.3 + 0.04 + 0.006 

(iv) 20 + 8 + 0.4 + 0.02 + 0.009

(v) 80 + 2 + 0.0 + 0.03 + 0.001

(vi) 20 + 9 + 0.0 + 0.07 + 0.009

(vii) 90 + 7 + 0.4 + 0.05 + 0.008

(viii) 40 + 9 + 0.3 + 0.00 + 0.009

(ix) 300 + 10 + 8 + 0.0 + 0.07 + 0.003

(x) 500 + 10 + 8 + 0.3 + 0.01 + 0.008

(xi) 300 + 20 + 7 + 0.2 + 0.00 + 0.009

(xii) 200 + 10 + 4 + 0.3 + 0.04 + 0.002

(xiii) 600 + 10 + 7 + 0.8 + 0.02 + 0.009

(xiv) 900 + 70 + 0 + 0.0 + 0.07 + 0.009

(xv) 200 + 10 + 4 + 0.3 + 0.04 + 0.002

(xvi) 600 + 50 + 2 + 0.4 + 0.09 + 0.003

VIII. Write the following expanded form of decimals into short form of decimals / Express as decimals:

(i) 200 + 40 + 3 + 0.2 + 0.04 + 0.006

(ii) 100 + 60 + 5 + 0.3 +0.05 + 0.008

(iii) 60 + 6 + 0.7 + 0.08 + 0.009

(iv) 500 + 90 + 2 + 0.2 + 0.04 + 0.006

(v) 90 + 7 + 0.4 +0.01 + 0.007

(vi) 8 + 3/10 + 7/100 + 1/1000

(vii) 30 + 9 + 6/10 + 9/100 + 2/1000

(viii) 700 + 80 + 5 + 1/10 + 4/100 + 7/1000

Answer:

VIII. (i) 243.246

(ii) 165.358

(iii) 66.789

(iv) 592.246

(v) 97.417

(vi) 8.371

(vii) 39.692

(viii) 785.147

● 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

5th Grade Math Problems

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