There are four different methods involved in dividing decimals:

- Division of a decimal number by a whole number
- Division of a decimal number by powers of 10
- Division of a decimal number by another decimal number

### Division of a decimal number by a whole number

While dividing a decimal number, we can follow the long division method used in division of whole numbers. The only difference is that a decimal point is placed in the quotient such that it lines up with the decimal point in the dividend.

### Examples on Dividing Decimals by a Whole Number

Given below are some examples that explains how to divide a decimal number by a whole number.

**Example 1: **

Divide 8.241 by 3

**Step 1:** Write the decimal number as a whole number, without considering the decimal point.

**Step 2:** Place the decimal point in the quotient such that it lines up with the given decimal number (dividend).

We can see that $\frac{8241}{3}$ = 2747

Hence, we get, $\frac{8.241}{3}$ = 2.747

And so, $\frac{82.41}{3}$ = 27.47

And, $\frac{824.1}{3}$ = 274.7

The decimal point of the quotient has to line up with that of the divisor.

**Example 2:**

Divide 9.346 by 7.

In this example, the remainder does not become zero. This is a case of non-terminating decimal. We may stop division at any stage depending on the accuracy required.

### Division of a decimal number by powers of 10

Consider the example 42.5 divided by 10.

42.5 = $\frac{425}{10}$

$\frac{42.5}{10}$ = $\frac{425}{10}$ / $\frac{10}{1}$

= $ \frac{425}{10}$ x $\frac{1}{10}$ (Multiplying by the reciprocal of $\frac{10}{1}$)

= $\frac{425}{100}$

= 4.25

We see that the digits of the divisor and the quotient are the same here, but the decimal point is shifted one place towards the left.

When we divide by 10, the decimal point will shift one place to the left. When we divide by 100, the decimal point will shift 2 places towards the left.

While dividing a decimal number by powers of 10, the digits of the decimal number and the quotient will be same but the decimal point in the quotient will be shifted to the left by as many places as the power of 10 ( the number of zeros in the power of 10)### Examples on Dividing Decimals by Powers of 10:

Given below are examples that explain division of decimal numbers by powers of 10.

**Example 1:**

Divide 89.998 by 1000

**Solution:**

Following the method of division of a decimal number by powers of 10, we will get the same quotient as the dividend. But, the decimal point will be shifted to the left by as many places as the number of zeros in the divisor.

$\frac{89.998}{1000}$ = 0.089998, because the decimal point should be shifted 3 places to the left.

$\frac{89.998}{1000}$ = 0.089998

**Example 2: **

Find the quotient of $\frac{203967}{100000}$

**Solution:**

Following the method of division, we get,

$\frac{203967}{100000}$ = 2.03967

### Dividing a decimal number by another decimal number

We can divide a decimal number by another decimal number through the following steps:

**Step 1:** Convert the divisor to a whole number by multiplying it by suitable powers of 10.

**Step 2:** While multiplying the divisor by a power of ten, we have to multiply the dividend also by the same power of 10.

**Step 3:** Now, we have to divide a decimal number by a whole number. Use the steps to divide a decimal number by a whole number.### Examples on Dividing Decimals by another Decimal Number

Given below are some examples on dividing a decimal number by a decimal number.

**Example 1:**

Divide $\frac{20.6816}{8.992}$

**Solution:**

**Step 1:** Convert the divisor to a whole number by multiplying it by a suitable power of 10.

The divisor is 8.992. We have to convert this as 8.992 x 1000 = 8992

**Step 2:** While multiplying the divisor by a power of ten, we have to multiply the dividend also by the same power of 10.

20.6816 x 1000 = 20681.6

**Step 3:** Now, we have to divide a decimal number by a whole number. Use the steps to divide a decimal number by a whole number.

Now, we have to find $\frac{20681.6}{8992}$

We know that, $\frac{206816}{8992}$ = 23

Hence, $\frac{20681.6}{8992}$ = 2.3

**Example 2:**

Find the answer to $\frac{35.568}{7.8}$

**Solution:**

Following the steps of division, we get

$\frac{35.568}{7.8} = \frac{(35.568\times10)}{(7.8)\times10}$

$ = \frac{355.68}{78}$

We have to divide 35568 by 78, and put the decimal point in the quotient such that it lines up with that of the dividend.

$\frac{35568}{78}$ = 456

Hence, $\frac{355.68}{78}$ = 4.56

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