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.