Mathematics • Year 7 • Unit 1 • Lesson 10
Decimals: Place Value and Rounding
Build the basics: read tenths / hundredths / thousandths, compare decimals by adding trailing zeros, and round using "look right — 5 or more, round up; less than 5, leave it".
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. Round 3.8472 to 2 decimal places.
Step 1 — Find the target digit (the one in the place you're rounding to).
3.8472 → tenths = 8, hundredths = 4, thousandths = 7, ten-thousandths = 2.
Target (2 d.p.) = hundredths digit = 4.
Reason: 2 decimal places means we want exactly 2 digits after the decimal point. The last of those is the hundredths.
Step 2 — Look at the digit immediately to the right of the target.
Next digit (the thousandths) = 7.
Reason: only that single digit decides whether the target digit goes up or stays.
Step 3 — Apply the rounding rule.
7 ≥ 5, so round the 4 UP to 5.
Reason: 5 or more rounds up; less than 5 stays the same.
Step 4 — Drop all digits after the target.
3.8472 → 3.85.
Answer: 3.85. (Sanity check: 3.85 is between 3.84 and 3.86, and closer to the upper end — that matches the rounding-up move.)
2. We do — fill in the missing steps
Same structure as Section 1, but for comparing two decimals. Fill in each blank line. 4 marks
Problem. Which is bigger: 0.608 or 0.62?
Step 1 — Write both with the same number of decimal places (add trailing zeros if needed):
0.608 stays as _____. 0.62 becomes _____.
Step 2 — Compare digit by digit, left to right:
Tenths: 6 vs 6 → _____.
Hundredths: _____ vs _____ → first difference!
Step 3 — Decide which is bigger from that first difference:
Since _____ > _____ in the hundredths column, _____ is bigger.
Step 4 — State the answer with the correct symbol: 0.608 _____ 0.62.
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation, the middle two are standard, and the last two are extension.
Foundation — single step
3.1 In 5.234, what is the value of the digit 3? 1 mark
3.2 Place >, < or = between: 0.5 ____ 0.45. 1 mark
3.3 Round 4.83 to 1 decimal place. 1 mark
3.4 Round 2.146 to 2 decimal places. 1 mark
Standard — combine two ideas
3.5 Write these decimals in order from smallest to largest: 0.45, 0.405, 0.5, 0.045. Show one column where the order changed. 2 marks
3.6 Round 6.8495 to (a) 1 d.p. and (b) 2 d.p. Show working for each. 2 marks
Extension — push your thinking
3.7 Convert 0.375 to a fraction in simplest form. Show: (a) write as 375/1000, (b) simplify using the HCF. 3 marks
3.8 Convert 3/8 to a decimal. (Hint: change the denominator to 1000 first.) 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (0.608 vs 0.62)
Step 1: 0.608 stays 0.608. 0.62 becomes 0.620.
Step 2: Tenths: 6 = 6 (equal). Hundredths: 0 vs 2 → first difference.
Step 3: Since 2 > 0 in the hundredths column, 0.62 is bigger.
Step 4: 0.608 < 0.62.
3.1 — Value of digit 3 in 5.234
The 3 sits in the hundredths column, so its value is 0.03 (or 3/100).
3.2 — 0.5 vs 0.45
Write 0.5 as 0.50. Tenths: 5 vs 4 — first difference. 5 > 4, so 0.5 > 0.45. Answer: 0.5 > 0.45.
3.3 — Round 4.83 to 1 d.p.
Target = 8 (tenths). Next digit = 3 (hundredths). 3 < 5, so 8 stays. Drop the 3. Answer: 4.8.
3.4 — Round 2.146 to 2 d.p.
Target = 4 (hundredths). Next digit = 6. 6 ≥ 5, so round 4 up to 5. Answer: 2.15.
3.5 — Order from smallest to largest
Write all with 3 decimal places: 0.450, 0.405, 0.500, 0.045.
Tenths: 4, 4, 5, 0. So 0.045 is smallest, 0.500 is largest. Between 0.450 and 0.405: hundredths 5 vs 0, so 0.405 < 0.450.
Order: 0.045 < 0.405 < 0.45 < 0.5. The hundredths column was the deciding column for 0.405 vs 0.45.
3.6 — Round 6.8495
(a) 1 d.p.: target = 8, next = 4. 4 < 5, so 8 stays. Answer: 6.8.
(b) 2 d.p.: target = 4, next = 9. 9 ≥ 5, so 4 rounds up to 5. Answer: 6.85.
3.7 — 0.375 as a fraction
(a) 0.375 = 375/1000.
(b) HCF(375, 1000) = 125. 375 ÷ 125 = 3; 1000 ÷ 125 = 8. So 0.375 = 3/8.
3.8 — 3/8 as a decimal
Multiply top and bottom by 125: 3/8 = (3 × 125)/(8 × 125) = 375/1000 = 0.375.