Converting Decimals to Fractions: Fifth Grade Mathematics

Converting decimals to fractions relies on reading the decimal using proper place value names and simplifying the resulting fraction to lowest terms.

The Three-Step Conversion Algorithm

Every terminating decimal can be converted into a fraction or mixed number using three systematic steps:
1. Identify the place value of the final digit on the far right (tenths, hundredths, or thousandths).

2. Write the digits as the numerator over that place value (10, 100, or 1,000) as the denominator.

3. Simplify the fraction to lowest terms by dividing by the Greatest Common Factor (GCF).

+--------------------------------------------------------------------------+
|                  DECIMAL TO FRACTION CONVERSION TABLE                    |
+---------+--------------------+-------------------+-----------------------+
| Decimal | Proper Word Name   | Unsimplified Frac | Simplest Form (GCF)   |
+---------+--------------------+-------------------+-----------------------+
| 0.8     | 8 tenths           | 8/10              | 4/5   (divide by 2)   |
| 0.45    | 45 hundredths      | 45/100            | 9/20  (divide by 5)   |
| 0.125   | 125 thousandths    | 125/1,000         | 1/8   (divide by 125) |
| 0.04    | 4 hundredths       | 4/100             | 1/25  (divide by 4)   |
+---------+--------------------+-------------------+-----------------------+

Watching the Place Value of Leading Zeros

When converting decimals with zeros immediately after the decimal point (like 0.06 or 0.008), the place value is determined strictly by the position of the final digit.
- In 0.06, the 6 is in the hundredths place: 6/100 = 3/50.

- In 0.008, the 8 is in the thousandths place: 8/1,000 = 1/125.

- Writing 6/10 for 0.06 is a major error because 6/10 = 0.6.

Converting Decimals Greater Than One to Mixed Numbers

When a decimal has a whole number portion (e.g., 3.75):
- Keep the whole number 3 as the whole number of the mixed number.

- Convert the decimal portion 0.75 to a fraction: 75/100.

- Simplify 75/100 to 3/4.

- Combine the parts: 3 3/4.

Converting 5.035 to a Mixed Number:
  Whole number: 5
  Decimal part: 0.035 = 35 thousandths = 35/1,000
  Simplify 35/1,000 by dividing by GCF (5):
    (35 / 5) / (1,000 / 5) = 7/200
  Final Mixed Number: 5 7/200

Exercises and Solutions

Exercise 1: Decimal to Fraction in Simplest Form. Convert 0.64 into a fraction in simplest form. Show the unsimplified fraction and the simplification process using the GCF.

Solution 1: The decimal 0.64 reads as "sixty-four hundredths" because the last digit 4 is in the hundredths place. Write 64 over 100: 64/100. Find the GCF of 64 and 100: factors of 64 include 1, 2, 4, 8, 16, 32, 64; factors of 100 include 1, 2, 4, 5, 10, 20, 25, 50, 100. The GCF is 4. Divide both terms by 4: 64 / 4 = 16, and 100 / 4 = 25. The fraction in simplest form is 16/25.

Exercise 2: Converting Decimals Greater Than One. Convert the measurement 4.375 into a mixed number in simplest form.

Solution 2: Keep the whole number 4. Examine the decimal portion 0.375: the final digit is in the thousandths place, so write 375/1,000. Find the GCF of 375 and 1,000: both numbers are divisible by 125 (375 / 125 = 3; 1,000 / 125 = 8). The GCF is 125. Dividing both numerator and denominator by 125 gives 3/8. Combine the whole number with the simplified fraction: 4 3/8.