Early rounding is one of the most common reasons a correct method produces a slightly wrong answer. Keep every value exact, or stored in full, until the last step, then round once.
This page shows the problem in two worked examples, then a routine that removes it. The non-calculator working trainer gives extra practice in exact steps, and the percentage-base explorer shows how rounded percentages drift.
What does “using the calculator too early” mean?
It means typing a result, reading a short version such as 0.69, and using that short version in the next line. The calculator’s display holds many more digits, and the ones you discard do not vanish. They are multiplied in every later step.
Think of a photocopy of a photocopy. Each copy loses a little detail, and after three copies the writing is unclear.
Worked example 1: a fraction that should cancel
Question: Work out 4.8 ÷ 7 × 14.
The early-rounding route.
4.8 ÷ 7 = 0.6857… The student writes 0.69.
Then 0.69 × 14 = 9.66.
The exact route. Rewrite the division as a fraction and cancel:
4.8 ÷ 7 × 14 = (4.8 × 14) ÷ 7 = 4.8 × 2 = 9.6
What went wrong. Dividing by 7 and then multiplying by 14 should give exactly “times 2”. Rounding 0.6857 to 0.69 shifted the value by about 0.004, and multiplying by 14 magnified that to about 0.06. The answer 9.66 looks close but is wrong.
Worked example 2: a root that should be exact
Question: Find the exact value of √50 × √2.
The early-rounding route.
√50 = 7.0710… and √2 = 1.4142… Rounding each to 2 decimal places gives 7.07 × 1.41 = 9.9687.
The student writes 9.97.
The exact route. Multiply inside one root: √50 × √2 = √100 = 10.
What went wrong. The exact answer is a whole number. Rounded inputs produced an answer that looks reasonable but hides that. A question that asks for an exact value should never be answered by a rounded decimal.
A routine that removes the problem
Use these four habits every time a question has more than one step.
- Look for cancellation first. Before pressing anything, ask whether a factor can cancel, as in example 1.
- Keep the exact form. Leave fractions, roots and π as they are until the last line.
- Store, do not retype. If you must use a decimal, store the full calculator value, and recall it in the next step instead of typing a short copy.
- Round once, at the end, and say so. Write the unrounded value, then the rounded answer, for example 9.6 or 9.687… ≈ 9.69 to 3 s.f.
Also check the size of your answer with an estimate. In example 1, 5 ÷ 7 × 14 is about 10, so 9.6 is plausible and so is 9.66. Estimation catches large errors, not tiny drifts, so the exact routine still matters.
A third situation: percentages in steps
Early rounding also happens with percentages. A price of RM 79 rises by 15%, then the new price falls by 15%.
- Exact: 79 × 1.15 = 90.85. Then 90.85 × 0.85 = 77.2225, so the final price is RM 77.22 to the nearest sen.
- Rounded too early: the student rounds 90.85 to 91, then 91 × 0.85 = 77.35. The answer is 13 sen too high.
Keep the unrounded 90.85 (or store it) through to the end. See successive increases and decreases and why rises and falls do not cancel.
Check yourself
1. Work out 3.6 ÷ 9 × 27 exactly.
Show answer
Cancel: 3.6 × 27 ÷ 9 = 3.6 × 3 = 10.8. Rounding 3.6 ÷ 9 = 0.4 is exact here, so either route works, which shows why you should spot cancellation before choosing a route.
2. A student computes √18 × √8 by rounding each root to 2 decimal places and writes 12. What is the exact value, and why might 12 be a risky answer?
Show answer
√18 × √8 = √144 = 12. The rounded route gives 4.24 × 2.83 = 11.9992, which rounds to 12, so the result here happens to survive. The risk is that the student never saw the exact value, and with slightly different roundings the final digit would change.
Where to go next
Exact arithmetic is taught in number sense and exact arithmetic, and comparing exact and approximate answers is a good next lesson. The assessment guide explains where to check your paper’s calculator rules.
If you already keep exact values but the drift still appears when you work quickly, a teacher can watch your line-by-line working in online one-to-one Mathematics tuition and find the moment the rounding enters.