Mathematics • Year 8 • Unit 1 • Lesson 2
Converting Between FDP
Build fluency with the step-by-step conversion methods from Lesson 2: fraction → decimal by division, decimal → percentage by × 100, and back the other way. Includes recurring decimals.
1. I do, fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. Convert 3/8 to a decimal and to a percentage.
Step 1, Spot which conversion comes first.
Fraction → decimal → percentage. The decimal sits in the middle.
Reason: the lesson's anchor: a/b → divide → decimal → × 100 → percentage.
Step 2, Divide top by bottom.
3 ÷ 8 = 0.375
Reason: the fraction bar IS a division sign. Use long division or a calculator, 8 goes into 3 zero times, then 30 ÷ 8 = 3 rem 6, then 60 ÷ 8 = 7 rem 4, then 40 ÷ 8 = 5 exactly.
Step 3, Decide if it terminates or recurs.
Remainder hit 0 after three digits → TERMINATING decimal.
Reason: when the remainder reaches 0 the division stops cleanly. (Denominators built from only 2s and 5s always terminate.)
Step 4, Multiply by 100 for the percentage.
0.375 × 100 = 37.5%
Reason: "%" means "out of 100", so multiplying by 100 turns a decimal into a percentage. The decimal point moves two places to the right.
Answer: 3/8 = 0.375 = 37.5%.
2. We do, fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. Convert 1/3 to a decimal and to a percentage. Watch out, this one recurs.
Step 1, Divide top by bottom:
1 ÷ 3 = 0.____ ____ ____ ...
Step 2, Does the remainder reach 0? ____________ . What digit keeps coming back? ______
Step 3, Write using recurring-decimal notation:
1/3 = 0.___ (with a bar over the recurring digit)
Step 4, Convert to percentage by × 100:
0.333... × 100 = ______ % (you may write it as 33.3...%)
3. You do, independent practice
Show your working in the space under each problem. The first four are foundation (single conversion, clean numbers). The middle two are standard (involve a recurring decimal or simplifying). The last two are extension (multi-step or explain).
Foundation, single conversion
3.1 Convert 1/4 to a decimal. 1 mark
3.2 Convert 0.4 to a percentage. 1 mark
3.3 Convert 25% to a decimal. 1 mark
3.4 Convert 7/10 to a decimal AND a percentage. 1 mark
Standard, recurring or simplify
3.5 Convert 2/3 to a decimal using recurring notation, then to a percentage. 2 marks
3.6 Convert 45% to a fraction over 100, then simplify using the HCF. 2 marks
Extension, multi-step / explain
3.7 Convert 5/8 to a decimal AND a percentage. State whether the decimal terminates or recurs, and explain in one sentence why. 3 marks
3.8 A student writes 6% = 0.6. Explain in one or two sentences why this is wrong, then give the correct decimal for 6%. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2, We do (faded 1/3)
Step 1: 1 ÷ 3 = 0.3 3 3 ...
Step 2: No, the remainder never reaches 0. The digit 3 keeps coming back.
Step 3: 1/3 = 0.3̄ (a bar over the 3 means it repeats forever).
Step 4: 0.333... × 100 = 33.3̄% (or approximately 33.3%).
3.1-1/4 as a decimal
1 ÷ 4 = 0.25.
3.2-0.4 as a percentage
0.4 × 100 = 40%. (Decimal point shifts two places right.)
3.3-25% as a decimal
25% = 25 ÷ 100 = 0.25. (Decimal point shifts two places left.)
3.4-7/10
7 ÷ 10 = 0.7. As a percentage: 0.7 × 100 = 70%. So 7/10 = 0.7 = 70%.
3.5-2/3
2 ÷ 3 = 0.666... = 0.6̄. As a percentage: 0.666... × 100 = 66.6̄% (about 66.7%).
3.6-45% as a simplified fraction
45% = 45/100. HCF of 45 and 100 is 5: 45 ÷ 5 = 9, 100 ÷ 5 = 20. So 45% = 9/20.
3.7-5/8
5 ÷ 8 = 0.625. As a percentage: 62.5%. The decimal terminates because the denominator 8 = 2 × 2 × 2 has only 2 as a prime factor, that always gives a terminating decimal.
3.8-6% ≠ 0.6
The student moved the decimal point only one place. "%" means "out of 100", so to convert to a decimal you divide by 100, which moves the point two places left. Correct: 6% = 6 ÷ 100 = 0.06. (Quick check: 0.6 = 60%, not 6%.)