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Multiplication-Decimal Numbers

Contents

  • 1 Multiplying a Decimal Fraction by a Whole number:
    • 1.1 Multiplication-Decimal Numbers Example 1:
    • 1.2 Multiplication-Decimal Numbers Example 2:
  • 2 Multiplying a Decimal Fractions by Numbers like 10, 100 and 1000 and their multiples:
    • 2.1 Multiplication-Decimal Numbers Example 3:
    • 2.2 Multiplication-Decimal Numbers Example 4:
    • 2.3 Multiplication-Decimal Numbers Example 5:
  • 3 Multiplying two Decimal Numbers, two Decimal Fractions:
    • 3.1 Multiplication-Decimal Numbers Example 6:
    • 3.2 Multiplication-Decimal Numbers Example 7:
    • 3.3 Properties of Multiplication of Decimal Fractions:

Multiplying a Decimal Fraction by a Whole number:

Step 1) Perform the multiplication treating them as ordinary numbers, ignoring the decimal point.
Step 2) Note the number of decimal places in the decimal number being multiplied.
Step 3) Put the decimal point in the product before as many digits from the right as the total number of decimal places in the decimal number being multiplied.

Multiplication-Decimal Numbers Example 1:

Find the product of 7.8 and 5.

Solution:

multiplication-of-decimals1

Write 1 5/8 as a decimal … The fraction 1 5/8 is equal to 1.875 when converted to a decimal.

Multiplication-Decimal Numbers Example 2:

Find 5.023 x 139.

Solution:

multiplication-of-decimals2

5.023 x 139 = 698.197. Similarly, 5023 x 0.139 = 698.197

Multiplying a Decimal Fractions by Numbers like 10, 100 and 1000 and their multiples:

When a decimal is multiplied by a number like 10, 100 or 1000, its decimal point gets shifted right as many places as there are zeros in the multiplier. If the number of digits in the decimal part is less than the number of places to shift, zeros are put in to make up the difference.

Multiplication-Decimal Numbers Example 3:

Find 9.38 x 10.

Solution:

multiplication-of-decimals3

That’s literally all there is to it! 9/20 as a decimal is 0.45

Multiplication-Decimal Numbers Example 4:

Find 48.765 x 100.

Solution:

multiplication-of-decimals4

Multiplication-Decimal Numbers Example 5:

Find 75.089 x 1000.

Solution:

multiplication-of-decimals5

Multiplying two Decimal Numbers, two Decimal Fractions:

 

We can multiply two decimal numbers/fractions as whole numbers and then put in the decimal point in the product.
Step 1) Perform the multiplication treating them as ordinary numbers, ignoring the decimal point.
Step 2) Note the number of decimal places in the multiplicand and multiplier.
Step 3) Put the decimal point in the product before as many digits from the right as the total number of decimal places in the multiplicand and multiplier.

We can also find the product of two decimal fractions by first converting them to common fractions and then multiplying them. The products we get by the two methods should tally.

Multiplication-Decimal Numbers Example 6:

 

Find 0.7 x 2.45.

Solution:

multiplication-of-decimals6

Multiplication-Decimal Numbers Example 7:

 

Find 6.15 x 3.1.

Solution:

multiplication-of-decimals7

Properties of Multiplication of Decimal Fractions:

The product of decimals in any order is the same.
For example, 0.5 x 1.6 = 1.6 x 0.5 = 0.80 = 0.8
The product of a decimal fraction and a whole number in any order is the same.
For example, 6.25 x 20 = 20 x 6.25 = 125
decimal x 1 = same decimal
1 x decimal = same decimal
For example, 0.68 x 1 = 0.68
1 x 0.75 = 0.75
The products of three or more decimals (or a combination of decimals and other numbers) grouped in different ways are the same.
For example, 5 x (3.02 x 9.9) = (5 x 3.02) x 9.9 = (5 x 9.9) x 3.02

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