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.

$Expanded form of Decimal$

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.

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

III. 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) 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 + $\frac{7}{100}$

IV. 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:

(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

V. 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:

(i) 16.309

(ii) 627.137

(iii) 2008.39

(iv) 471.572

(v) 5080.202

VI. 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:

VI. (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

2. 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:

2. (i) 9.462

(ii) 640.005

(iii) 303. 502

(iv) 747.023

3. 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:

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

(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 + + + $\frac{5}{\mathbf{{\color{Red}100}}}$ + $\frac{3}{\mathbf{{\color{Red}1000}}}$

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