Dividing Decimals

Dividing Decimals is similar to dividing whole numbers, except for the way we handle the decimal point. When we divide decimals, we change the divisor to a whole number by moving the decimal point all the way to the right. Then, we move the decimal point of the dividend up to the same number of places to the right and divide the resultant numbers in the normal way as we do regular division.

Let us learn more about the division of decimals by reading the content given below, which will help us to understand this better.

Decimals are a part of the extended number system to express tenths, hundredths, thousandths, and so on. Working with decimals may seem a bit complex but the various operations using decimal numbers is quite similar to the operations using whole numbers. A decimal number has a whole number part and the fractional part separated by a dot. The digits following the decimal point show a value smaller than one.

For example, 24.15 is a decimal number with 24 in its number part and 15 in the decimal part. This can be understood with the following explanation: 24.15= 20 + 4 + 0.1 + 0.05.

The process of dividing decimals is similar to the normal division process, but we just need to keep in mind the decimal point which should be correctly placed in the quotient. Since we are referring to decimals, the following steps will help us to understand the process of dividing decimals.

• To divide a decimal number by a whole number, the division is performed in the same way as in the whole numbers. We first divide the two numbers ignoring the decimal point. Then, the decimal point in the quotient is placed in the same position as in the dividend. For example, 18.2 ÷ 2 = 9.1
• To divide a decimal number by a decimal number, multiply the divisor by as many tens as necessary until we get a whole number, and remember to multiply the dividend by the same number of tens. For example, 13.8 ÷ 0.6 becomes 138 ÷ 6 = 23.

Dividing Decimals by Whole Numbers: Dividing decimals by whole numbers is similar to the normal division. Here the dividend is a decimal and the divisor is a whole number, so the quotient will have the number of decimals based on the decimals in the dividend. The division of decimals with a whole number is easily done by taking the following steps.

• Step 1: For example to divide 78.92 ÷ 4, ignore the decimal and divide normally until you get 0 as the remainder.
• Step 2: Place the decimal point in the quotient in the same position as given in the dividend. 78.92 ÷ 4=19.73. Thus, we get 19.73 as the answer, where the decimal is placed according to the decimal of the dividend.

Dividing Decimals by another Decimal Number: In this division, both the dividend and the divisor are decimals and we can solve them by two methods. In the first method, we first move the decimals of the divisor to make it a whole number, and then we move the decimals of the dividend. Let us understand this with the help of the following steps:

• Step 1: For example, to divide 48.5 by 3.5, move the decimal of the divisor to the right as many times as necessary to make it a whole number. This makes the divisor 35.
• Step 2: Move the decimal in the dividend up to the same number of digits as you moved it in the divisor. This makes the divisor 485.
• Step 3: Now, divide the dividend (485) by the divisor (35) just like regular division.

The second method is used when the number of digits after the decimal in the dividend is more or less than the number of decimals in the divisor.

If the dividend's decimal place is more than or equal to the divisor's decimal place:

• Step 1: Ignore the decimal and divide normally until you get 0 as the remainder. For example, to divide: 0.09 ÷ 0.3, we ignore the decimals and write it as 9 ÷ 3= 3.
• Step 2: Place the decimal point using the formula: Dividend's decimal place - Divisor's decimal place= Quotient's decimal place. Now, using the formula, we get 2-1 =1. Hence, the decimal of the quotient will be placed as 0.3

If the dividend's decimal place is less than the divisor's decimal place: In this case, convert the decimal to a fraction. For example: 0.4 ÷ 0.02 = 4/10 ÷ 2/100 = 4/10 × 100/2 = 20.

The long division with decimals can be easily done just as the normal long division. The following sequence of steps explains the process of long division of decimals.

• First, write the division in the standard form. Start by dividing the whole number part by the divisor.
• Place the decimal point in the quotient above the decimal point of the dividend. Bring down the tenth digit.
• Divide and bring down the other digit in sequence. Divide until 0 is obtained in the remainder. Thus, the decimal in the quotient is similar is equal to the decimal in the dividend.

Now, let us look at the following tips that are helpful while dividing decimals.

• Convert the divisor to a whole number by multiplying by the powers of 10. Multiply the dividend by the same powers of 10.
• When you divide a decimal number by 10, move the decimal point to the left by one place.
• When you divide a decimal number by 100, move the decimal point to the left by two places.
• When you divide a decimal number by 1000, move the decimal point to the left by three places.

Related Topics

• Relationship Between Fractions and Decimals
• Decimals and Fractions
• Addition and Subtraction of Decimals

FAQs on Dividing Decimals