Decimal Division Explanation and Examples

When dividing decimal fractions you may encounter several cases.

Decimal fraction by natural number

To divide the decimal fraction by a natural number, we use the following rules.

1. We divide the decimal fraction by a natural number according to the rules of division into a column, not paying attention to the comma.
2. We put in a private comma, when the division of the whole part of the dividend ends.

If the integer part of the dividend is less than the divisor, then in the private part we put 0 integers.

Example:

Note that the integer part of the decimal fraction (we have 0) is less than the divisor (31). Therefore, in the private we immediately put 0 in the whole part.

Do not forget to record the answer in the example:

Examples:

• 310.1: 10 = 31.01
• 27.56: 100 = 0.2756
• 0.75: 10 = 0.075

Division of a natural number into a decimal fraction

1. We count the number of characters to the right of the decimal point in decimal.
2. Multiply both the dividend and the divisor by 10, 100, or 1000, etc., to turn the decimal fraction into an integer.
3. We divide numbers as natural.

Example:

We count the number of decimal places in decimal. We have one sign. So, to turn 2.5 into an integer, you need to multiply it by 10. Do not forget and the dividend multiply by 10.

5: 2.5 = (5 • 10): (2.5 • 10) = 50: 25 = 2

Dividing decimals into each other

You can divide decimal fractions in different ways. We describe one of the possible. By tradition, a small plan of action:

1. Determine the fraction with the largest number of characters (digits) to the right of the comma.

2. Multiply both decimals by 10, 100, 1000, etc., to turn decimals into integers.

3. We divide ordinary numbers by the rules of division into a column and write the answer.

Example:

• The greatest number of digits (figures) after the decimal point is in the first decimal fraction, so we focus on it. To turn 7.44 into an integer, multiply it by 100 (see multiplication of decimal fractions).

  
  

  At 10, 100, 1000, etc. both decimals are multiplied.
  And they are multiplied by the same number. That is, if you multiplied the first fraction by 10, then you must multiply the second by 10.

  

• Multiply each of the decimal fractions by 100.

  

• We divide ordinary numbers into a column and write the answer. Remember that we initially divided the decimal fractions .

  

• 25.37: 0.001 = 25.37 • 1 000 = 25 370
• 0.08: 0.1 = 0.08 • 10 = 0.8