# Decimal

A fractional number whose denominator is 10 or multiple of 10 is called a decimal. Every decimal has two parts whole number part and decimal part. These two parts are separated by a dot or point. This dot or point is known as decimal point.

For example, 51.731 is decimal. Here 51 is the whole part and 731 is the decimal part.

The length of a pencil is 17.2 cm. This is read as seventeen point two cm.

A decimal is read in two ways:

(i) 43.814 is read as forty three point eight, one, four.

(ii) 43.814 is read as forty three and eight hundred fourteen thousandths.

How to write a fractional number as decimals?

7/10 = .07

2179/1000 = 2.179

How to write a decimal as fractional numbers?

To convert a decimal number 49.50 into a fraction, 49.50 = 4950/100.

Similarly,

(i) 1.1 = 11/10

(ii) 2.13 = 213/100

(iii) 17.2 = 172/10

(iv) 14.11 = 1411/100

(v) 9.781 = 9781/1000

So, from the above explanation we conclude that the number is divided:

(a) by 10 if there is one digit after the decimal.

(b) by 100 if there is two digits after the decimal.

(c) by 1000 if there is three digits after the decimal.

(d) by 10000 if there is three digits after the decimal and so on.

(a) The number is divided by 10 if there is one digit after the decimal.

For example:

(i) 1.5 = 15/10

[We observe that in 1.5, after the decimal there is one digit so we need to divide by 10]

(ii) 12.3 = 123/10

[We observe that in 12.3, after the decimal there is one digit so we need to divide by 10]

(iii) 10.1 = 101/10

[We observe that in 10.1, after the decimal there is one digit so we need to divide by 10]

(iv) 111.2 = 1112/10

[We observe that in 111.2, after the decimal there is one digit so we need to divide by 10]

(v) 145.9 = 1459/10

[We observe that in 145.9, after the decimal there is one digit so we need to divide by 10]

(b) The number is divided by 100 if there is two digits after the decimal.

For example:

(i) 2.51 = 251/100

[We observe that in 2.51, after the decimal there is two digits so we need to divide by 100]

(ii) 12.03 = 1203/100

[We observe that in 12.03, after the decimal there is two digits so we need to divide by 100]

(iii) 19.11 = 1911/100

[We observe that in 19.11, after the decimal there is two digits so we need to divide by 100]

(iv) 11.24 = 1124/100

[We observe that in 11.24, after the decimal there is two digits so we need to divide by 100]

(v) 14.93 = 1493/100

[We observe that in 14.93, after the decimal there is two digits so we need to divide by 100]

(c) The number is divided by 1000 if there is three digits after the decimal.

For example:

(i) 1.555 = 1555/1000

[We observe that in 1.555, after the decimal there is three digits so we need to divide by 1000]

(ii) 12.005 = 12005/1000

[We observe that in 12.005, after the decimal there is three digits so we need to divide by 1000]

(iii) 2.001 = 2001/1000

[We observe that in 2.001, after the decimal there is three digits so we need to divide by 1000]

(iv) 1.112 = 1112/1000

[We observe that in 1.112, after the decimal there is three digits so we need to divide by 1000]

(v) 15.913 = 15913/1000

[We observe that in 15.913, after the decimal there is three digits so we need to divide by 1000]

Decimal Place Value Chart.

Expanded form of Decimal Fractions.

Like Decimal Fractions.

Unlike Decimal Fraction.

Equivalent Decimal Fractions.

Changing Unlike to Like Decimal Fractions.

Comparison of Decimal Fractions.

Conversion of a Decimal Fraction into a Fractional Number.

Conversion of Fractions to Decimals Numbers.

Subtraction of Decimal Fractions.

Multiplication of a Decimal Numbers.

Multiplication of a Decimal by a Decimal.

Properties of Multiplication of Decimal Numbers.

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.

Conversion of fraction to Decimal Fraction.

Simplification in Decimals.

Word Problems on Decimal.