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How to Divide Decimals with Decimals Without A Calculator

Reviewed by Calculator Editorial Team

Dividing decimals can seem tricky, but with the right method, you can do it without a calculator. This guide explains how to divide decimals by decimals step-by-step, including examples and a built-in calculator.

How to Divide Decimals

Dividing decimals follows the same basic rules as dividing whole numbers, but with an extra step to account for the decimal places. Here's the general method:

  1. Move the decimal point in both numbers to the right until they become whole numbers.
  2. Divide the whole numbers as you normally would.
  3. Place the decimal point in the quotient directly above where it was in the original dividend.

This method ensures that the decimal places are properly accounted for in the final result.

Step-by-Step Method

Step 1: Align the Decimal Points

First, count the number of decimal places in both the dividend (number being divided) and the divisor (number you're dividing by). Then, move the decimal point in both numbers to the right until they become whole numbers.

Example

Divide 0.6 by 0.2:

  • 0.6 has 1 decimal place
  • 0.2 has 1 decimal place
  • Move both decimal points right by 1 place: 6 ÷ 2

Step 2: Perform the Division

Now that both numbers are whole numbers, perform the division as you normally would. For the example above, 6 ÷ 2 = 3.

Step 3: Place the Decimal Point

The quotient (result) will have the same number of decimal places as the original numbers had combined. In our example, both original numbers had 1 decimal place, so the result is 3.0, which we can simplify to 3.

Formula

To divide two decimals:

  1. Count decimal places in dividend (D) and divisor (d)
  2. Multiply both by 10max(D,d) to make them whole numbers
  3. Divide the whole numbers: (dividend × 10max(D,d)) ÷ (divisor × 10max(D,d))
  4. Place decimal point in result with max(D,d) decimal places

Common Mistakes

When dividing decimals, it's easy to make these common errors:

  • Forgetting to move the decimal point in both numbers
  • Moving the decimal point in only one number
  • Counting the decimal places incorrectly
  • Placing the decimal point in the wrong position in the result

Double-checking your work can help avoid these mistakes.

Practical Examples

Example 1: 0.8 ÷ 0.4

  1. Both numbers have 1 decimal place
  2. Move decimal right by 1: 8 ÷ 4
  3. 8 ÷ 4 = 2
  4. Result: 2.0 (simplified to 2)

Example 2: 0.75 ÷ 0.25

  1. Both numbers have 2 decimal places
  2. Move decimal right by 2: 75 ÷ 25
  3. 75 ÷ 25 = 3
  4. Result: 3.00 (simplified to 3)

Example 3: 1.2 ÷ 0.3

  1. Dividend has 1 decimal place, divisor has 1 decimal place
  2. Move decimal right by 1: 12 ÷ 3
  3. 12 ÷ 3 = 4
  4. Result: 4.0 (simplified to 4)

FAQ

Do I need to move the decimal point in both numbers?
Yes, you must move the decimal point in both the dividend and the divisor the same number of places to maintain the relationship between them.
How do I know how many places to move the decimal?
Count the number of decimal places in both numbers and move the decimal point in both numbers to the right until they become whole numbers.
What if the numbers have different numbers of decimal places?
Move the decimal point in both numbers to the right until they both have the same number of decimal places as the original number with the most decimal places.
How do I place the decimal point in the result?
The result should have the same number of decimal places as the original numbers combined. Place the decimal point directly above where it was in the original dividend.