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How to Turn Fraction Into Decimal Without Calculator

Reviewed by Calculator Editorial Team

Converting fractions to decimals is a fundamental math skill that's useful in many real-world situations. Whether you're working on homework, budgeting, or measuring ingredients, knowing how to perform this conversion without a calculator can save time and build confidence in your math abilities.

Methods to Convert Fractions to Decimals

There are several reliable methods to convert fractions to decimals without a calculator. The two most common approaches are:

  1. Long division method
  2. Equivalent fractions method

Both methods are effective, but the long division method is generally more straightforward for most fractions. We'll explore both methods in detail below.

Long Division Method

The long division method involves dividing the numerator by the denominator to find the decimal equivalent. Here's a step-by-step guide:

  1. Write the fraction as a division problem (numerator ÷ denominator)
  2. Divide the numerator by the denominator
  3. If there's a remainder, add a decimal point and zeros to continue dividing
  4. Continue the process until you either get a remainder of zero or the decimal repeats

Example: Convert 3/4 to a decimal using long division.

  1. 4 goes into 3 zero times, so write 0. and add a 0 to make 30
  2. 4 goes into 30 seven times (4 × 7 = 28), write 7 after the decimal point
  3. Subtract 28 from 30 to get a remainder of 2
  4. Add another 0 to make 20, and 4 goes into 20 five times (4 × 5 = 20)
  5. Subtract 20 from 20 to get a remainder of 0
  6. The decimal equivalent is 0.75

This method works well for both terminating and repeating decimals. For repeating decimals, you'll notice the same sequence of digits repeating after the decimal point.

Equivalent Fractions Method

The equivalent fractions method involves finding a fraction with the same value but a denominator that's a power of 10 (like 10, 100, 1000, etc.). Here's how it works:

  1. Identify the denominator of your fraction
  2. Find a number that, when multiplied by the denominator, results in a power of 10
  3. Multiply both the numerator and denominator by this number
  4. The resulting fraction will have a denominator that's a power of 10, making it easy to write as a decimal

Example: Convert 1/8 to a decimal using equivalent fractions.

  1. The denominator is 8. We need to find a number that, when multiplied by 8, gives a power of 10. 125 works because 8 × 125 = 1000.
  2. Multiply numerator and denominator by 125: (1 × 125)/(8 × 125) = 125/1000
  3. Now we can write 125/1000 as 0.125

This method is particularly useful when dealing with fractions that have denominators that are factors of powers of 10. It can be faster than long division for these cases.

Worked Examples

Let's look at a few examples to see how these methods work in practice.

Example 1: Terminating Decimal

Convert 5/8 to a decimal.

Long Division Method:

  1. 8 goes into 5 zero times, write 0. and add a 0 to make 50
  2. 8 goes into 50 six times (8 × 6 = 48), write 6 after the decimal point
  3. Subtract 48 from 50 to get a remainder of 2
  4. Add another 0 to make 20, and 8 goes into 20 two times (8 × 2 = 16)
  5. Subtract 16 from 20 to get a remainder of 4
  6. Add another 0 to make 40, and 8 goes into 40 five times (8 × 5 = 40)
  7. Subtract 40 from 40 to get a remainder of 0
  8. The decimal equivalent is 0.625

Example 2: Repeating Decimal

Convert 1/3 to a decimal.

Long Division Method:

  1. 3 goes into 1 zero times, write 0. and add a 0 to make 10
  2. 3 goes into 10 three times (3 × 3 = 9), write 3 after the decimal point
  3. Subtract 9 from 10 to get a remainder of 1
  4. Add another 0 to make 10 again, and the pattern repeats
  5. The decimal equivalent is 0.333... (the 3 repeats indefinitely)

Example 3: Using Equivalent Fractions

Convert 3/5 to a decimal.

Equivalent Fractions Method:

  1. The denominator is 5. We need to find a number that, when multiplied by 5, gives a power of 10. 2 works because 5 × 2 = 10.
  2. Multiply numerator and denominator by 2: (3 × 2)/(5 × 2) = 6/10
  3. Now we can write 6/10 as 0.6

Frequently Asked Questions

How do I know if a fraction will convert to a terminating or repeating decimal?

A fraction will convert to a terminating decimal if the denominator (after simplifying) has no prime factors other than 2 or 5. If the denominator has any other prime factors, the decimal will repeat.

What if I get a remainder that never becomes zero?

If you're working with a repeating decimal, the division process will continue indefinitely with the same sequence of digits repeating. You can stop when you've identified the repeating pattern.

Is there a quick way to convert simple fractions to decimals?

Yes, for simple fractions like 1/2, 1/4, 1/5, 1/8, and 1/10, you can often recognize the decimal equivalent by memory. For example, 1/2 = 0.5, 1/4 = 0.25, and 1/5 = 0.2.

Can I use these methods for mixed numbers?

Yes, first convert the mixed number to an improper fraction, then apply either method. For example, to convert 1 1/2 to a decimal, first change it to 3/2, then proceed with the conversion.