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How to Divide Decimals Without Calculator

Reviewed by Calculator Editorial Team

Dividing decimals without a calculator can be challenging, but with the right methods, you can perform these calculations accurately. This guide explains two reliable techniques: converting decimals to whole numbers and using long division. We'll also provide worked examples to help you master this skill.

Method 1: Convert to Whole Numbers

One of the simplest ways to divide decimals is by converting them to whole numbers. This method involves moving the decimal point in both the dividend and divisor to eliminate the decimal places.

Steps:

  1. Count the number of decimal places in both the dividend and divisor.
  2. Move the decimal point in both numbers to the right until both become whole numbers.
  3. Divide the resulting whole numbers.
  4. Place the decimal point in the quotient directly above where it was placed in the dividend.

For example, to divide 0.6 by 0.2:

  1. Both numbers have one decimal place.
  2. Multiply both by 10 to get 6 and 2.
  3. Divide 6 by 2 to get 3.
  4. The answer is 3.

This method works well when both numbers have the same number of decimal places. If they don't, you'll need to adjust accordingly.

Method 2: Use Long Division

Long division is another effective method for dividing decimals. This technique involves setting up the division problem and performing the division steps as you would with whole numbers, then handling the decimal point separately.

Steps:

  1. Write the dividend inside the division bracket and the divisor outside.
  2. Divide as you would with whole numbers, bringing down digits one at a time.
  3. If the divisor doesn't go into the current digit, write 0 in the quotient and bring down the next digit.
  4. Continue until you've brought down all digits.
  5. If there's a remainder, add a decimal point to the dividend and continue bringing down zeros.
  6. Place the decimal point in the quotient directly above where it is in the dividend.

For example, to divide 1.2 by 0.4:

  1. Write 1.2 inside the bracket and 0.4 outside.
  2. 0.4 goes into 1.2 three times (0.4 × 3 = 1.2).
  3. The answer is 3.

Long division can be more time-consuming but is useful when dealing with decimals that don't easily convert to whole numbers.

Worked Examples

Let's look at a few examples to solidify your understanding.

Example 1: 0.8 ÷ 0.2

Using Method 1:

  1. Both numbers have one decimal place.
  2. Multiply both by 10 to get 8 and 2.
  3. Divide 8 by 2 to get 4.
  4. The answer is 4.

Example 2: 1.5 ÷ 0.3

Using Method 1:

  1. Both numbers have one decimal place.
  2. Multiply both by 10 to get 15 and 3.
  3. Divide 15 by 3 to get 5.
  4. The answer is 5.

Example 3: 2.4 ÷ 0.6

Using Method 2:

  1. Write 2.4 inside the bracket and 0.6 outside.
  2. 0.6 goes into 2.4 four times (0.6 × 4 = 2.4).
  3. The answer is 4.

Frequently Asked Questions

How do I divide decimals when the divisor has more decimal places than the dividend?

You can still use either method. For Method 1, you'll need to multiply both numbers by the same power of 10 to eliminate the decimals. For Method 2, proceed with long division as usual.

What if I get a remainder when dividing decimals?

If you have a remainder, you can continue the division by adding decimal places to the dividend and bringing down zeros until the remainder is zero or you have a repeating decimal.

Is there a quick way to check my decimal division?

Yes, you can multiply your answer by the divisor to see if you get back the dividend. This is a good way to verify your calculations.