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How to Divide Decimals by Decimals Without A Calculator Mcat

Reviewed by Calculator Editorial Team

Dividing decimals is a common math operation that appears frequently on standardized tests like the MCAT. While calculators are allowed on the MCAT, knowing how to perform decimal division manually can help you verify your answers and save time when a calculator isn't available.

Step-by-Step Method for Dividing Decimals

Follow these steps to divide one decimal by another without a calculator:

Step 1: Eliminate the Decimals

First, convert both numbers to whole numbers by multiplying them by the same power of 10. This will eliminate the decimal points.

Step 2: Perform the Division

Now that you have whole numbers, perform the division as you normally would. You can use long division or any other method you're comfortable with.

Step 3: Place the Decimal Point

Count the number of decimal places in both the original dividend and divisor. The sum of these decimal places will determine where to place the decimal point in your answer.

Step 4: Simplify the Fraction (if needed)

If your answer is a fraction, simplify it to its lowest terms. This is particularly important for MCAT problems where exact answers are often required.

Pro Tip: Practice with simple examples first, then gradually work with more complex numbers to build your confidence.

Worked Examples

Example 1: 0.6 ÷ 0.2

  1. Multiply both numbers by 10 to eliminate decimals: 6 ÷ 2
  2. Perform the division: 6 ÷ 2 = 3
  3. Count decimal places: 1 in 0.6 and 1 in 0.2 (total 2)
  4. Place decimal point: 3.00 (or simply 3)

Example 2: 0.75 ÷ 0.05

  1. Multiply both numbers by 100: 75 ÷ 5
  2. Perform the division: 75 ÷ 5 = 15
  3. Count decimal places: 2 in 0.75 and 2 in 0.05 (total 4)
  4. Place decimal point: 15.0000 (or simply 15)

Key Insight: The number of decimal places in the answer is equal to the number of decimal places in the dividend minus the number of decimal places in the divisor.

The Formula

To divide two decimals (A ÷ B):

  1. Count the number of decimal places in A (n)
  2. Count the number of decimal places in B (m)
  3. Multiply both numbers by 10max(n,m) to make them whole numbers
  4. Perform the division of the whole numbers
  5. Place the decimal point in the result so that it has (n - m) decimal places

This method ensures you get an accurate result every time, which is especially important for standardized tests where precision matters.

Frequently Asked Questions

Do I need to eliminate decimals before dividing?

Yes, eliminating decimals first makes the division process much simpler and reduces the chance of errors. It's the most reliable method for manual decimal division.

What if the numbers have different numbers of decimal places?

Multiply both numbers by the same power of 10 to match the number of decimal places. For example, 0.35 (2 decimal places) and 0.07 (2 decimal places) can both be multiplied by 100 to become 35 and 7.

How do I know where to place the decimal point in the answer?

Count the total number of decimal places in both the original dividend and divisor. The answer should have the same number of decimal places as the sum of these counts.

Can I use this method for division problems on the MCAT?

Absolutely! This method is perfect for MCAT math sections where you might need to verify answers or work through problems without a calculator.