1. Rounding to a Given Place Value
Rounding to place value means rounding to the nearest 10, 100, 1000, etc. This is different from decimal places.
The Four-Step Process
Rounding to Nearest 100
Step 1: Identify the digit in the place value you're rounding to (the hundreds digit)
Step 2: Circle the digit to the right (the tens digit)
Step 3: If circled ≥ 5, round UP. If circled < 5, round DOWN
Step 4: Replace all digits to the right with zeros
Example: 1567.45 to nearest 100
Circle the 6 (tens digit). Since 6 ≥ 5, round up.
Answer: 1600
Q: Round 2,534 to the nearest 100.
❌ Forgetting to write zeros — When rounding 2534 to nearest 100, the answer is 2500, NOT 25. The zeros are essential for place value!
2. Rounding to Decimal Places (d.p.)
Rounding to decimal places means counting positions after the decimal point (nearest tenth, hundredth, etc.).
Key Rules
✓ Rule 1: Always keep the required number of decimal places in your answer
✓ Rule 2: Do NOT drop trailing zeros after the decimal point
✓ Rule 3: 2.4 rounded to 2 d.p. is 2.40 (not 2.4)
Example: 2.435 to 2 d.p.
Identify 2nd decimal place: 3
Circle 3rd decimal: 5
Since 5 ≥ 5, round up (3 becomes 4)
Answer: 2.44
Example: 0.295631 to 2 d.p.
Identify 2nd decimal place: 9
Circle 3rd decimal: 5
Since 5 ≥ 5, round up (9 becomes 10, so 29 becomes 30)
Answer: 0.30 (the final zero is crucial!)
Q: Round 4.998 to 2 decimal places.
3. Rounding to Significant Figures (s.f.)
Significant figures count all digits from left to right, starting at the first non-zero digit.
Finding the First Significant Figure
3097: First s.f. is 3 (leftmost digit)
0.006207: First s.f. is 6 (leading zeros don't count)
0.03040: First s.f. is 3, and the zero after 4 DOES count
Rule: Leading zeros (before the first non-zero digit) are NOT significant. All other zeros (including trailing zeros in decimals) ARE significant.
Large Numbers
When rounding large numbers, fill up to the decimal point with zeros.
Example: 34,568 to 2 s.f. → 35,000 (NOT 35)
Decimals
For decimals, keep zeros between the decimal point and first s.f.
Example: 0.003435 to 3 s.f. → 0.00344
Q: Round 345,256 to 3 significant figures.
Q: Round 0.002956 to 3 significant figures.
Why not write 253 instead of 345,000? Because 253 and 345,000 are completely different sizes! The zeros show place value and are essential.
4. Degree of Accuracy for Answers
Different questions require different levels of rounding. Always read the question carefully.
Answer Types
Exact answers: Leave as simplified fraction, π, or square root. Don't round.
Specified accuracy: Round to whatever the question asks (2 d.p., 3 s.f., etc.)
No accuracy specified: