Page 206 - New Medley 5 Semester 1

Multiplication of Decimals

Multiplying a Decimal by a Whole Number

Pragya filled a big container with water using a small bucket. She uses

the bucket 8 times to fill the container completely. If the bucket can hold
3.675 L of water, find the volume of water of the big container.

Here, we can add 3.675 L up to 8 times or multiply 3.675 L by 8.

i.e., 3.675 L + 3.675 L + 3.675 L + ... 8 times = 3.675 L × 8

To multiply a decimal by a whole number, proceed as follows:

1. Multiply the numbers, ignoring the decimal point.

2. Count the digits in decimal parts. There
3675
are 3 decimal places in the multiplier.
× 8

3. Put the decimal point in the product 29400
after 3 places from the right. 3.675 → 3 decimal places

Thus, the volume of water in the big container  3.675 × 8 = 29.400
is 29.400 L or 29.4 L.

Example 10: Multiply 18.37 by 26.

Solution: 1 8 . 3 7 → 2 decimal places

× 2 6

1 1 0 2 2
3 6 7 4

4 7 7 . 6 2 ← Put a decimal after 2 digits from the right

Multiplying a Decimal by 10, 100 and 1000

Observe the following multiplications:

As 428 × 10 = 4280, So, 4.28 × 10 = 42.80, i.e., 42.80 or 42.8

As 428 × 100 = 42800, So, 4.28 × 100 = 428.00, i.e., 428.00 or 428

As 428 × 1000 = 428000, So, 4.28 × 1000 = 4280.00, i.e., 4280.00 or 4280

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