Expressing Fractions as Decimals
Semester 4B · Chapter 12 · Lesson 6 · MATH-4B-C12-L06
Before you begin: prerequisite check
Recall: 4A fraction equivalence. Attempt these questions independently first.
Write 0.97 as a fraction in simplest form.
Show answer and reasoning
0.97 = 97/100. Reduce by the common factor 1 to 97/100.
Write 0.53 as a fraction in simplest form.
Show answer and reasoning
0.53 = 53/100. Reduce by the common factor 1 to 53/100.
Write 0.04 as a fraction in simplest form.
Show answer and reasoning
0.04 = 4/100. Reduce by the common factor 4 to 1/25.
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 fraction whose denominator can be converted to ten or one hundred can be written as a decimal. For example, 3/5 = 6/10 = 0.6, while 7/20 = 35/100 = 0.35. Multiply the numerator and denominator by the same whole number so the fraction stays equivalent. Some denominators cannot produce an exact finite tenths/hundredths representation. Do not force a simple terminating decimal where the fraction needs more precision.
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 1/5 as a decimal.
Rename 1/5 in tenths or hundredths (or divide numerator by denominator) to get 0.2.
Check 1: try it yourself
Write 27/50 as a decimal.
Show answer and reasoning
Rename 27/50 in tenths or hundredths (or divide numerator by denominator) to get 0.54.
Worked example 2
Write 1/10 as a decimal.
Rename 1/10 in tenths or hundredths (or divide numerator by denominator) to get 0.1.
Check 2: try it yourself
Write 44/50 as a decimal.
Show answer and reasoning
Rename 44/50 in tenths or hundredths (or divide numerator by denominator) to get 0.88.
Worked example 3
Write 17/50 as a decimal.
Rename 17/50 in tenths or hundredths (or divide numerator by denominator) to get 0.34.
Check 3: try it yourself
Write 2/5 as a decimal.
Show answer and reasoning
Rename 2/5 in tenths or hundredths (or divide numerator by denominator) to get 0.4.
Guided practice
Write 13/50 as a decimal.
Show answer and reasoning
Rename 13/50 in tenths or hundredths (or divide numerator by denominator) to get 0.26.
Write 47/50 as a decimal.
Show answer and reasoning
Rename 47/50 in tenths or hundredths (or divide numerator by denominator) to get 0.94.
Write 12/50 as a decimal.
Show answer and reasoning
Rename 12/50 in tenths or hundredths (or divide numerator by denominator) to get 0.24.
Write 2/4 as a decimal.
Show answer and reasoning
Rename 2/4 in tenths or hundredths (or divide numerator by denominator) to get 0.5.
Write 14/20 as a decimal.
Show answer and reasoning
Rename 14/20 in tenths or hundredths (or divide numerator by denominator) to get 0.7.
Independent practice
Write 2/25 as a decimal.
Show answer and reasoning
Rename 2/25 in tenths or hundredths (or divide numerator by denominator) to get 0.08.
Write 6/10 as a decimal.
Show answer and reasoning
Rename 6/10 in tenths or hundredths (or divide numerator by denominator) to get 0.6.
Write 8/10 as a decimal.
Show answer and reasoning
Rename 8/10 in tenths or hundredths (or divide numerator by denominator) to get 0.8.
Write 5/25 as a decimal.
Show answer and reasoning
Rename 5/25 in tenths or hundredths (or divide numerator by denominator) to get 0.2.
Write 4/5 as a decimal.
Show answer and reasoning
Rename 4/5 in tenths or hundredths (or divide numerator by denominator) to get 0.8.
Write 3/5 as a decimal.
Show answer and reasoning
Rename 3/5 in tenths or hundredths (or divide numerator by denominator) to get 0.6.
Write 32/50 as a decimal.
Show answer and reasoning
Rename 32/50 in tenths or hundredths (or divide numerator by denominator) to get 0.64.
Write 1/2 as a decimal.
Show answer and reasoning
Rename 1/2 in tenths or hundredths (or divide numerator by denominator) to get 0.5.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Write 4/5 as a decimal. Explain how place value or a model can check your result.
Show answer and reasoning
Rename 4/5 in tenths or hundredths (or divide numerator by denominator) to get 0.8. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “A fraction with denominator 4 becomes a decimal by just writing a decimal point before 4.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 1/4 = 25/100 = 0.25; convert the amount, not the printed denominator. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Write 3/50 as a decimal.
Show answer and reasoning
Rename 3/50 in tenths or hundredths (or divide numerator by denominator) to get 0.06.
Write 3/4 as a decimal.
Show answer and reasoning
Rename 3/4 in tenths or hundredths (or divide numerator by denominator) to get 0.75.
Write 3/10 as a decimal.
Show answer and reasoning
Rename 3/10 in tenths or hundredths (or divide numerator by denominator) to get 0.3.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.