# Properties of Multiplication of Decimal Numbers

We will discuss here all the properties of multiplication of decimal numbers.

1. The product of a decimal and a whole number multiplied in any order remains the same.

For Example:

(i) 0.9 × 12 = 12 × 0.9 = 10.8

(ii) 1.1 × 30 = 30 × 1.1 = 33.0

(iii) 2.1 × 14 = 14 × 2.1 = 29.4

(iv) 1.8 × 11 = 11 × 1.8 = 19.8

(v) 0.7 × 17 = 17 × 0.7 = 11.9

2. The product of two decimal numbers remains the same, even if the order is changed.

For Example:

(i) 2.5 × 3.5 = 3.5 × 2.5 = 8.75

(ii) 1.4 × 0.8 = 0.8 × 1.4 = 1.12

(iii) 4.2 × 2.1 = 2.1 × 4.2 = 8.82

(iv) 0.5 × 1.5 = 1.5 × 0.5 = 0.75

(v) 3.7 × 1.9 = 1.9 × 3.7 = 7.03

3. The product of a decimal fraction and 1 is the decimal fraction itself.

For Example:

(i) 1.092 × 1 = 1.092

(ii) 1.002 × 1 = 1.002

(iii) 12.619 × 1 = 12.619

(iv) 2.519 × 1 = 2.519

(v) 0.127 × 1 = 0.127

4. The product of a decimal fraction and zero is zero.

For Example:

(i) 891.56 × 0 = 0

(ii) 1.009 × 0 = 0

(iii) 0.008 × 0 = 0

(iv) 42.19 × 0 = 0

(v) 16.35 × 0 = 0

5. While performing multiplication in decimals, the numbers can be taken in any order and the product remains the same.

For Example:

 (i) 1.02 × (11.2 × 2.3) = 1.02 × 25.76= 26.2752 (1.02 × 2.3) × 11.2 = 2.346 × 11.2= 26.2752

So the product of more than two decimals does not change if their grouping order is changed.

Therefore, 1.02 × (11.2 × 2.3) = (1.02 × 2.3) × 11.2

(ii) (1.20 × 0.3) × 1.18                   =                    0.3 × (1.18 × 1.20)

0.36 × 1.18                               =                    0.3 × 1.416

0.4248                                      =                    0.4248

Therefore, (1.20 × 0.3) × 1.18 = 0.3 × (1.18 × 1.20)

Since, we know the product of two decimals or more does not change if their grouping order is changed.

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.

Comparison of Decimal Fractions.

Conversion of a Decimal Fraction into a Fractional Number.

Conversion of Fractions to Decimals Numbers.

Addition of Decimal Fractions.

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.