Round to 1 Significant Figure First, Then Calculate
Estimation method: round each value to 1 s.f. → then perform the simpler calculation
Estimation means finding an approximate answer by rounding first. This is faster than exact calculation and helps you check that an answer is in the right ballpark.
Example 1 — Estimate \(38 \times 21\)
Step 1
Round each to 1 significant figure: \(38 \approx 40\) and \(21 \approx 20\)
Step 2
Calculate the rounded version: \(40 \times 20 = 800\)
Step 3
Answer: \(\approx 800\). (Actual: 798 — very close.)
Example 2 — Estimate \(489 \div 52\)
Step 1
Round each to 1 s.f.: \(489 \approx 500\), \(52 \approx 50\)
Tip: Round to 1 significant figure for estimation — this keeps numbers easy to work with mentally.
✓ Quick Check 1 — Estimating by rounding to 1 s.f.
Question 1 of 10
Checking Answers — Is It "About Right"?
After completing a calculation, use estimation to check if your answer is reasonable. If your estimate and your answer are very different, you may have made an error.
Example 3 — A student calculates \(48 \times 52 = 24{,}960\). Is this reasonable?
The student's answer is 24,960 — about 10 times too large.
Step 3
A decimal point error has likely occurred. The correct answer is 2,496.
Example 4 — A student buys 6 items at £8.95 each and gets a total of £537. Is this right?
Step 1
Estimate: \(6 \times £9 = £54\).
Step 2
£537 is about 10 times too large — likely a decimal error.
Step 3
Correct answer: \(6 \times £8.95 = £53.70\).
Common mistake: Accepting a calculator answer without checking it makes sense. Always estimate first so you can spot errors immediately.
✓ Quick Check 2 — Checking answers and spotting errors
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Extension — beyond FS2 level: Upper and lower bounds are not required for the Functional Skills Level 2 exam. This section is included for learners who want to go further.
Upper and Lower Bounds (Extension)
When a measurement is rounded, the true value could be anywhere in a range. The upper bound is the largest value that would round to the given figure. The lower bound is the smallest.
Lower bound = given value − (half the rounding unit)
Upper bound = given value + (half the rounding unit)
Example 5 — A rope is measured as 12 m to the nearest metre. Find the upper and lower bounds.
Step 1
Rounding unit is 1 m. Half of 1 m = 0.5 m.
Step 2
Lower bound: \(12 - 0.5 = 11.5\) m
Step 3
Upper bound: \(12 + 0.5 = 12.5\) m
Step 4
True length: \(11.5 \leq \text{length} < 12.5\) m
Example 6 — A bag of flour weighs 500 g to the nearest 10 g. Find the bounds.
In real life: Engineers use the upper bound for safety-critical calculations (e.g., maximum load on a bridge). They never assume the smallest possible value when safety is at stake.
✓ Quick Check 3 — Upper and lower bounds (Extension)
Question 1 of 10
Practice: Estimation and Approximation
Estimate each calculation by rounding to 1 significant figure. Type your estimate.
#
Question
Answer
Result
1
38 × 21
2
297 + 412
3
489 ÷ 52
4
6.8 × 4.3
5
72 × 49
6
810 ÷ 38
7
5.2 × 9.7
8
386 × 21
9
612 − 289
10
9.4 × 3.1
⚠ Things to Watch Out For
Rounding to an unhelpful degree: For estimation, round each number to 1 significant figure first. 38 × 21 → 40 × 20 = 800. This gives a quick, reasonable estimate.
Assuming the estimate is the answer: Estimation is a CHECK, not a replacement for the accurate answer. Use it to spot errors, not to avoid calculation.
Rounding all numbers the same way: Sometimes rounding one number up and another down gives a better estimate than both up or both down.
Upper/lower bound confusion: The upper bound is the LARGEST value that would round to the given figure. For 5 (to nearest 1): lower = 4.5, upper = 5.5 (not included).
Forgetting units: An estimate of "800" means nothing without units. Always include the unit in your estimated answer.