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

You are watching: 9/1000 as a decimal

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

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 expandedform:

(i) 3479.105

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

= 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 + 1thousandths

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

(vi) 840.006

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

= 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 decimalfractions:

(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 fractionalexpansion.

One example has been done for you to get the idea how to dodecimals 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

(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 decimalexpansion.

One example has been done for you to get the idea how to dodecimals 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

(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 givenbelow.

(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

(i) 16.309

(ii) 627.137

(iii) 2008.39

(iv) 471.572

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

● 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.

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.

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