How to Divide Decimals?

Here we will learn How to Divide Decimals?

I. Dividing a Decimal by a Whole Number:

1. Divide 25.6 by 4.

Solution:

Step I: Divide as usual without considering the decimal point. (256 ÷ 4 = 64)

Step II: Count the number of decimal places in the dividend. Here, it is 1.

Step III: Insert the decimal point after 1 digit from the right in the quotient.

            64 → 6.4

Answer: 6.4

2. Divide 25.6 by 4.

Solution:

We place o in the quotient as whole number, if the whole number in the dividend is smaller than the divisor.

Answer: 0.75

3. Divide 24.64 by 8.

Solution:

Step I: Divide as usual without considering the decimal point. (2464 ÷ 8 = 308)

Step II: Count the number of decimal places in the dividend. Here, it is 2.

Step III: Insert the decimal point after 2 digits from the right in the quotient.

            308 → 3.08

We place the decimal point in the quotient after two digits from the right as it is placed in the dividend.

Answer: 3.08

II. Dividing a Decimal by another Decimal:

If the dividend and divisor are both decimal numbers, we multiply both the numbers by 10, 100, 1000, etc. so that the divisor becomes a whole number. Then we divide as usual Let us consider some examples.

1. Divide 4.096 by 0.32

Solution:

   4.096 ÷ 0.32

= \(\frac{4.096}{0.32}\)

= \(\frac{4.096}{0.32}\) × \(\frac{100}{100}\)

= \(\frac{409.6}{32}\)

We multiply the dividend and divisor both by 100 to make the divisor a whole number.

We place the decimal point just after one digit from the right as dividend 409.6 has the decimal point just after one digit from the right.

Answer: 12.8

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2. Divide 0.168 by 1.2

Solution:

   0.168 ÷ 1.2

= \(\frac{0.168}{1.2}\)

= \(\frac{0.168}{1.2}\) × \(\frac{10}{10}\)

= \(\frac{1.68}{12}\)

We multiply the dividend and divisor both by 10 to make the divisor a whole number.

We place the decimal point after two digit from the right as dividend 1.68 has the decimal point after two digit from the right.

Answer: 0.14

III. Dividing a Decimal by 10, 100 and 1000:

To divide a decimal by 10, 100 and 1000, we shift the point to the left according to the number of zeros in the divisor. While shifting the point, if there are not enough digits in the dividend, we add zeros to the extreme left to get the required number of digits. Let us consider an example.

1. Divide 23.4 by (i) 10, (ii) 100 and (iii) 1000.

Solution.

(i) 23.4 ÷ 10 = 2.34

(Decimal point is shifted to one place to the left because 10 has only one zero.)

(ii) 23.4 ÷ 100 = 0.234

(Decimal point is shifted to two places to the left because 100 has two zeros.)

(iii) 23.4 ÷ 1000 = 0.0234

(Decimal point is shifted to three places to the left because 1000 has three zeros. We add one zero to the extreme left to the dividend for having the required number of digits.)

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