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.
Expanded form of 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.
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 10, 100, 1000
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 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.
5th Grade Numbers Page
5th Grade Math Problems
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