Converting Fractions and Decimals Worksheets
The guided notes Converting Fractions and Decimals worksheets include a lesson, homework, and answer key to help you learn or teach this concept. Click HERE for the free download of the lesson on TpT.
Before learning to convert fractions to decimals and decimals to fractions, let’s first learn the different types of decimals. Different decimals will require a different approach to converting them to fractions.
Types of Decimals
There are three main types of decimals:
- Terminating decimal: a decimal that terminates.
- Repeating decimal: a decimal that repeats.
- Non-terminating/non-repeating decimal: a decimal that does not terminate or repeat.
Below is a chart with different types of decimals, their definitions, and examples:
Convert fractions to terminating decimals
To convert fractions to terminating decimals, divide the numerator by the denominator. You can either use a calculator or long division.
Steps to Follow:
Divide the numerator by the denominator.
USING A CALCULATOR
Step 1: Press [3] [รท] [8][๐ฐ] & [enter].
USING LONG DIVISION
See the example in the chart below to follow along as you read the steps
Step 1: Find how many times does 8 go into 3. Write that number above the division bracket.
Step 2: Add a “0” to the right of the 3 and a decimal point to the right of the “0” above.
Step 3: Find how many times does 8 go into 30. The answer is 3 times. Write a 3 to the right of the decimal point above. 8 times 3 is 24, hence subtract 24 from 30. The remainder is 6. Add a “0” to the right of 6.
Step 4: Find how many times does 8 go into 60. The answer is 7. Write 7 next to the 3 above the division bracket. Multiply 8 times 7. Which gives 56. Subtract 56 from 60. The remainder is 4.
Step 5: Add a “0” to the right of the 4. Find how many times does 8 go into 40. The answer is 5 times. Write a 5 next to the 7 above the division bracket. Subtract 40 from 40. The remainder is “0”.
NOTE: When a fraction converts to a terminating decimal, the remainder will always be “0”.
Converting terminating decimals to fractions
Steps to Follow:
Step 1: Place the decimal over its place value: tenths, hundredths, or thousandths.
Step 2: Simplify the fraction. Identify the greatest common factor (GCF). Then, divide the numerator and the denominator by the GCF to reduce the fraction. For example, for 2/10, the GCF is “2”. Both the numerator and the denominator can be divided by 2. When 2/10 is reduced, the simplified fraction is 1/5. This fraction is simplified as the numerator and denominator have no common factors besides 1.
Converting repeating decimals to fractions
Steps to Follow:
Step 1: Set the repeating decimal equal to variable ๐.
Step 2: Multiply both sides of the equation by 10^n (10 to the power of ๐), where ๐ is the number of repeating digits.
Step 3: Subtract ๐ from both sides.
Step 4: Solve for ๐ and simplify.
I hope this helps!
