Converting Fractions to Decimals: Fifth Grade Mathematics

Converting fractions into decimals connects division, place value, and powers of ten.

Two Methods for Converting Fractions to Decimals

There are two primary methods to convert a fraction into a decimal: Converting to a Power-of-Ten Denominator, and Long Division.

+--------------------------------------------------------------------------+
|                  FRACTION TO DECIMAL CONVERSION METHODS                  |
+---------------------+----------------------------------------------------+
| Method              | When and How to Apply                              |
+---------------------+----------------------------------------------------+
| Power-of-Ten        | Best when denominator is a factor of 10, 100, or   |
| Denominator         | 1,000 (e.g., 2, 4, 5, 20, 25, 50). Multiply to get |
|                     | 10, 100, or 1,000 in denominator.                  |
| Long Division       | Universal method; divide numerator by denominator  |
| (Numerator / Denom) | (Numerator inside bracket, denominator outside).   |
+---------------------+----------------------------------------------------+

Method 1: Friendly Denominators (Powers of Ten)

If the denominator can be multiplied to produce 10, 100, or 1,000, find an equivalent fraction and write it directly as a decimal:
- Denominator 5: 3/5 = (3 * 2) / (5 * 2) = 6/10 = 0.6

- Denominator 4: 3/4 = (3 * 25) / (4 * 25) = 75/100 = 0.75

- Denominator 8: 5/8 = (5 * 125) / (8 * 125) = 625/1,000 = 0.625

- Denominator 20: 7/20 = (7 * 5) / (20 * 5) = 35/100 = 0.35

Friendly Factor Pairs for Powers of 10:
  2  * 5   = 10
  4  * 25  = 100
  5  * 20  = 100
  8  * 125 = 1,000

Method 2: Long Division (Universal Method)

For any fraction a/b, divide a by b. Place a decimal point and annexed zeros after the numerator.

Converting 3/8 by Long Division:

             0 . 3 7 5
         +------------
       8 | 3 . 0 0 0
         - 2   4
         -------
               6 0
             - 5 6
             -----
                 4 0
               - 4 0
               -----
                   0

       3/8 = 0.375

Converting Mixed Numbers to Decimals

To convert a mixed number like 4 3/5 to a decimal, keep the whole number part intact (4) and convert the fractional part (3/5 = 0.6). Combine them: 4 + 0.6 = 4.6.

Exercises and Solutions

Exercise 1: Power-of-Ten Conversion. Convert the fraction 9/25 into a decimal by creating an equivalent fraction with a power-of-ten denominator. Show all work.

Solution 1: Identify what factor multiplies the denominator 25 to reach 100: 25 * 4 = 100. Multiply both the numerator and denominator by 4: (9 * 4) / (25 * 4) = 36/100. The fraction 36/100 represents thirty-six hundredths, which is written in standard decimal form as 0.36.

Exercise 2: Long Division Conversion. Convert 5/8 into a decimal using long division. Show each step of dividing, bringing down zeros, and placing the decimal point.

Solution 2: Write 5 as 5.000 inside the division bracket with 8 outside. Place the decimal point in the quotient directly above the decimal in 5.000. 8 goes into 5 zero times. 8 goes into 50 six times (6 * 8 = 48; 50 - 48 = 2). Bring down 0 to make 20. 8 goes into 20 two times (2 * 8 = 16; 20 - 16 = 4). Bring down 0 to make 40. 8 goes into 40 five times (5 * 8 = 40; 40 - 40 = 0). The division terminates with a remainder of 0. Thus, 5/8 = 0.625.