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 + 1/10 + 2/100 + 9/1000


Again,

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

         = 400 + 90 + 3 + 2/10


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

             = 1000 + 400 + 30 + 6 + 7/10 + 4/100

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


1. Write in expanded form:

(i) 3479.105

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

= 3000 + 400 + 70 + 9 + 1/10 + 0/100 + 5/1000


(ii) 7833.45

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

= 7000 + 800 + 30 + 3 + 4/10 + 5/100


(iii) 21.1097

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

= 20 + 1 + 1/10 + 0/100 + 9/1000 + 7/10000


(iv) 524.1

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

= 500 + 20 + 4 + 1/10


(v) 143.011

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

= 100 + 40 + 3 + 0/10 + 1/100 + 1/1000


(vi) 840.006

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

= 800 + 40 + 0 + 0/10 + 0/100 + 6/1000


(vii) 64.21

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

= 60 + 4 + 2/10 + 1/100


(viii) 4334.334

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

= 4000 + 300 + 30 + 4 + 3/10 + 3/100 + 4/1000


2. Write as decimal fractions:

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

= 8008.39


(ii) 4000 + 7 + 5/10 + 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 + 9/100

= 451.09


(vi) 800 + 70 + 2 + 8/10 + 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.


Practice Problems 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) 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:

(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:

(i) 16.309

(ii) 627.137

(iii) 2008.39

(iv) 471.572

(v) 5000 + 80 + 0 + 0.2 + 0.002 5080.202

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