Fractions → Decimals: 5 Questions (each with sub-questions + answers)
Each question asks you to convert one or more fractions into decimal form. Answers include short steps and the final decimal. Use the overline bar shown for repeating decimals.
Question 1 — Simple terminating decimals
- a) Convert 1/2 to a decimal.
- b) Convert 3/4 to a decimal.
- c) Convert 5/8 to a decimal.
Answers & steps
a) 1/2
Step: divide 1 by 2 → 0.5.
Step: divide 3 by 4 → 0.75.
Step: divide 5 by 8 → 0.625.
Step: divide 1 by 2 → 0.5.
Final: 0.5
b) 3/4Step: divide 3 by 4 → 0.75.
Final: 0.75
c) 5/8Step: divide 5 by 8 → 0.625.
Final: 0.625
Question 2 — Mixed numbers & improper fractions
- a) Convert 7/4 to a decimal (improper fraction).
- b) Convert 2 1/3 (mixed number) to a decimal.
Answers & steps
a) 7/4
Step 1: divide 7 by 4 → 1 remainder 3. Step 2: continue as decimal: 3/4 = 0.75. So 1 + 0.75 = 1.75.
Step 1: convert to improper fraction: (2×3 + 1)/3 = 7/3. Step 2: divide 7 by 3 → 2 remainder 1. 1/3 is repeating: 0.. So result = 2.333...
Step 1: divide 7 by 4 → 1 remainder 3. Step 2: continue as decimal: 3/4 = 0.75. So 1 + 0.75 = 1.75.
Final: 1.75
b) 2 1/3Step 1: convert to improper fraction: (2×3 + 1)/3 = 7/3. Step 2: divide 7 by 3 → 2 remainder 1. 1/3 is repeating: 0.. So result = 2.333...
Final: 2. (that is 2.333...)
Question 3 — Repeating (recurring) decimals
- a) Convert 1/3 to a decimal and show the repeating part.
- b) Convert 2/11 to a decimal (identify repeating block).
Answers & steps
a) 1/3
Step: divide 1 by 3 → 0.333... The digit 3 repeats forever. Represent as 0..
Step: divide 2 by 11 → 0.181818... Here the two-digit block "18" repeats.
Step: divide 1 by 3 → 0.333... The digit 3 repeats forever. Represent as 0..
Final: 0. (0.333...)
b) 2/11Step: divide 2 by 11 → 0.181818... Here the two-digit block "18" repeats.
Final: 0. (0.1818...)
Question 4 — Convert then round
- a) Convert 7/20 to a decimal.
- b) Convert 13/25 to a decimal and round to two decimal places.
Answers & steps
a) 7/20
Step: divide 7 by 20 → 0.35 (terminating).
Step: divide 13 by 25 → 0.52 exactly. Rounding to two decimal places keeps 0.52.
Step: divide 7 by 20 → 0.35 (terminating).
Final: 0.35
b) 13/25Step: divide 13 by 25 → 0.52 exactly. Rounding to two decimal places keeps 0.52.
Final: 0.52 (rounded to 2 d.p. = 0.52)
Question 5 — Challenge: identify type then convert
- a) Is 9/12 terminating or repeating when converted? Convert it to a decimal (simplify first).
- b) Is 4/15 terminating or repeating? Convert to decimal and write repeating block if any.
Answers & steps
a) 9/12
Step 1: simplify: 9/12 = 3/4. 3/4 is terminating. Step 2: 3 ÷ 4 = 0.75.
Step: divide 4 by 15 → 0.2666... The repeating block is the digit 6 (after the initial 2). So decimal = 0.2 which equals 0.2666...
Step 1: simplify: 9/12 = 3/4. 3/4 is terminating. Step 2: 3 ÷ 4 = 0.75.
Final: 0.75 (terminating)
b) 4/15Step: divide 4 by 15 → 0.2666... The repeating block is the digit 6 (after the initial 2). So decimal = 0.2 which equals 0.2666...
Final: 0.2 (0.2666...)
