Expressing Decimals as Fractions in Simplest Form
Semester 4B · Chapter 12 · Lesson 5 · MATH-4B-C12-L05
Before you begin: prerequisite check
Recall: 4A equivalent and simplified fractions. Attempt these questions independently first.
Rename 0.4 as hundredths and write the equivalent decimal to two places.
Show answer and reasoning
Every tenth is ten hundredths; multiply the count by ten.
A student writes 0.8 = 0.80. Is this equation true, and why?
Show answer and reasoning
Both mean 80 hundredths. A trailing zero does not change the number.
How many hundredths are in 4 tenths?
Show answer and reasoning
Each tenth consists of 10 hundredths; 4×10=40.
Key vocabulary
- tenth
- one of ten equal parts of a whole
- hundredth
- one of one hundred equal parts
- equivalent decimals
- two notations for the same amount
- midpoint
- exact halfway point between rounding benchmarks
Understand the concept
A terminating decimal in tenths or hundredths is a fraction whose denominator is ten or one hundred. For example, 0.75 is 75/100, and dividing numerator and denominator by 25 gives 3/4. To write a decimal in simplest fractional form, first name its place-value fraction, then divide the numerator and denominator by their greatest common factor. Never simplify by changing only one of the two values: that would change the fraction's meaning.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
Write 0.02 as a fraction in simplest form.
0.02 = 2/100. Reduce by the common factor 2 to 1/50.
Check 1: try it yourself
Write 0.38 as a fraction in simplest form.
Show answer and reasoning
0.38 = 38/100. Reduce by the common factor 2 to 19/50.
Worked example 2
Write 0.52 as a fraction in simplest form.
0.52 = 52/100. Reduce by the common factor 4 to 13/25.
Check 2: try it yourself
Write 0.07 as a fraction in simplest form.
Show answer and reasoning
0.07 = 7/100. Reduce by the common factor 1 to 7/100.
Worked example 3
Write 0.53 as a fraction in simplest form.
0.53 = 53/100. Reduce by the common factor 1 to 53/100.
Check 3: try it yourself
Write 0.60 as a fraction in simplest form.
Show answer and reasoning
0.60 = 60/100. Reduce by the common factor 20 to 3/5.
Guided practice
Write 0.72 as a fraction in simplest form.
Show answer and reasoning
0.72 = 72/100. Reduce by the common factor 4 to 18/25.
Write 0.12 as a fraction in simplest form.
Show answer and reasoning
0.12 = 12/100. Reduce by the common factor 4 to 3/25.
Write 0.96 as a fraction in simplest form.
Show answer and reasoning
0.96 = 96/100. Reduce by the common factor 4 to 24/25.
Write 0.61 as a fraction in simplest form.
Show answer and reasoning
0.61 = 61/100. Reduce by the common factor 1 to 61/100.
Write 0.23 as a fraction in simplest form.
Show answer and reasoning
0.23 = 23/100. Reduce by the common factor 1 to 23/100.
Independent practice
Write 0.08 as a fraction in simplest form.
Show answer and reasoning
0.08 = 8/100. Reduce by the common factor 4 to 2/25.
Write 0.82 as a fraction in simplest form.
Show answer and reasoning
0.82 = 82/100. Reduce by the common factor 2 to 41/50.
Write 0.65 as a fraction in simplest form.
Show answer and reasoning
0.65 = 65/100. Reduce by the common factor 5 to 13/20.
Write 0.75 as a fraction in simplest form.
Show answer and reasoning
0.75 = 75/100. Reduce by the common factor 25 to 3/4.
Write 0.16 as a fraction in simplest form.
Show answer and reasoning
0.16 = 16/100. Reduce by the common factor 4 to 4/25.
Write 0.14 as a fraction in simplest form.
Show answer and reasoning
0.14 = 14/100. Reduce by the common factor 2 to 7/50.
Write 0.13 as a fraction in simplest form.
Show answer and reasoning
0.13 = 13/100. Reduce by the common factor 1 to 13/100.
Write 0.74 as a fraction in simplest form.
Show answer and reasoning
0.74 = 74/100. Reduce by the common factor 2 to 37/50.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Write 0.12 as a fraction in simplest form. Explain how place value or a model can check your result.
Show answer and reasoning
0.12 = 12/100. Reduce by the common factor 4 to 3/25. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “25/100 is already in simplest form.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: divide top and bottom by 25 to get 1/4. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Write 0.28 as a fraction in simplest form.
Show answer and reasoning
0.28 = 28/100. Reduce by the common factor 4 to 7/25.
Write 0.36 as a fraction in simplest form.
Show answer and reasoning
0.36 = 36/100. Reduce by the common factor 4 to 9/25.
Write 0.85 as a fraction in simplest form.
Show answer and reasoning
0.85 = 85/100. Reduce by the common factor 5 to 17/20.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.