# Properties of Multiplication of Decimal Numbers

This topic will deal with properties of multiplication of decimal numbers. These properties on multiplication of decimal numbers will help the learners to understand better. It will give them a different and unique insight into this topic of multiplication of decimal numbers. The properties on multiplication of decimal numbers will enrich their knowledge on this topic and thereby boost better understanding. Five very basic properties of multiplication of decimal numbers would help the learners in understanding the concept better along with few examples on each of the property discussed.

Here in this content we will discuss the properties on multiplication of decimal numbers:

Property I: If we multiply a decimal number with 1 the product will be the decimal number itself.

Here are few examples to illustrate the property:

Examples:

(i) 56.258 × 1 = 56.258

(ii) 784.244 × 1 = 784.244

(iii) 8850.45 × 1 = 8850.45

(iv) 15.06 × 1 =  15.06

(v) 19.743 × 1 =  19.743

Property II: If we change the order of multiplying a decimal number with a whole number the product remains the same.

Here are few examples to illustrate the property:

Examples:

(i) 23.52 × 11 = 11 × 23.52 = 258.72

(ii) 140.21 × 21 = 21 × 140.21 = 2944.41

(iii) 46. 12 × 6 = 6 × 46.12 = 276.72

(iv) 115.88 × 42 = 42 × 115.88 = 4866.96

(v) 59.10 × 16 = 16 × 59.10 = 945.60

Property III: If we change the order of multiplying a decimal number with another decimal number the product remains the same.

Here are few examples to illustrate the property:

Examples:

i) 78.74 × 54.21 = 54.21 × 78.74 = 426.4954

ii) 0.01 × 2.21 = 2.21 × 0.01 = 0.0221

iii) 25.14 × 3.2 = 3.2 × 25.14 = 80.448

iv) 14.96 × 7.8 = 7.8 × 14.96 = 116.88

v) 12.30 × 1.5 = 1.5 × 12.30 = 18.45

Property IV: If a decimal number is multiplied with 0 the product will be zero.

Here are few examples to illustrate the property:

Examples:

(i) 7.54 × 0 = 0

(ii) 19.86 × 0 = 0

(iii) 132.54 × 0 = 0

(iv) 44.13 × 0 = 0

(v) 112.25 × 0 = 0

Property V: If more than two decimal numbers are multiplied and we change the order of the decimal numbers the product remain the same.

Here are few examples to illustrate the property:

Examples:

(i) 25.26 × (1.4 × 2.3)

= 25.26 × 3.22

= 81.3372

On changing their grouping order of multiplication.

(1.4 × 25.26) × 2.3

= 35.364 × 2.3

= 81.3372

So we can see the on changing the order of grouping the product does not change.

(ii) 3.62 × (0.5 × 8.7)

= 3.62 × 4.35

= 15.747

On changing their grouping order of multiplication.

(8.7 × 3.62) × 0.5

= 31.494 × 0.5

= 15.747

So we can see the on changing the order of grouping the product does not change.