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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 + 110 + 2100 + 91000


Again,

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

         = 400 + 90 + 3 + 210


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

             = 1000 + 400 + 30 + 6 + 710 + 4100


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 + 110 + 0100 + 51000


(ii) 7833.45

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

= 7000 + 800 + 30 + 3 + 410 + 5100


(iii) 21.1097

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

= 20 + 1 + 110 + 0100 + 91000 + 710000


(iv) 524.1

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

= 500 + 20 + 4 + 110


(v) 143.011

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

= 100 + 40 + 3 + 010 + 1100 + 11000


(vi) 840.006

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

= 800 + 40 + 0 + 010 + 0100 + 61000


(vii) 64.21

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

= 60 + 4 + 210 + 1100


(viii) 4334.334

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

= 4000 + 300 + 30 + 4 + 310 + 3100 + 41000


2. Write as decimal fractions:

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

= 8008.39


(ii) 4000 + 7 + 510 + 6100

= 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 + 9100

= 451.09


(vi) 800 + 70 + 2 + 810 + 51000

= 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 + 510 + 4100 = 30 + 8 + 0.5 + 0.04


(ii) 83.107 = 83 + 110 + 0100 + 71000

                = 80 + 3 + 0.1 + 0 + 0.007

                = 80 + 3 + 0.1 + 0.007


(ii) 627.074 = 627 + 010 + 7100 + 41000

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

                  = 600 + 20 + 7 + 0.07 + 0.004


II. Write following in short form:

(i) 9 + 310 + 4100

(ii) 50 + 7 + 610 + 2100 + 41000

(iii) 100 + 4 + 310 + 61000


Solution:

(i) 9 + 310 + 4100 = 9.34

(ⅱ) 50 + 7 + 610 + 2100 + 41000 = 57.624

(iii) 100 + 4 + 310 + 61000 = 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 + 710 + 3100

(i) 23.8

(ii) 60.27

(iii) 119.05

(iv) 276.207


Answers:

I. (i) 20 + 3 + 810

(ii) 60 + 0 + 210 + 7100

(iii) 100 + 10 + 9 + 0 + 5100

(iv) 200 + 70 + 6 + 210 + 0 + 7100


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 + 310 + 91000

(ii) 600 + 20 + 7 + 110 + 3100 + 71000

(iii) 2000 + 8 + 310 + 9100

(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 + 🔲 + 210+ 9🔲

(ii) 35.265= 30 + 5 + 🔲10 + 6100 + 5🔲

(iii) 5672.053= 5000 + 600 + 🔲 + 🔲 + 5🔲3🔲


Answer:

VI. (i) 84.29 = 80 + 4 + 210 + 9100

(ii) 35.265= 30 + 5 + 210 + 6100 + 51000

(iii) 5672.053= 5000 + 600 + 70 + 2 + 5100 +  31000


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


IX. Write in decimal form.

(i) 800 + 40 + 6 + 1/10 + 3/100 + 4/1000

(ii) 9000 + 60 + 9 + 3/100 + 7/1000

(iii) 6000 + 200 + 3 + 4/10 + 3/100 + 5/1000

(iv) 9000 + 60 + 9 + 7/100 + 3/1000


Answer:

IX. (i) 846.134

(ii) 9069.037

(iii) 6203.435

(iv) 9069.073

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Changing Unlike to Like Decimal Fractions.

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Conversion of a Decimal Fraction into a Fractional Number.

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