A calculator shows more digits than any exam answer needs. Appropriate precision means giving the accuracy the question asks for, such as 3 significant figures or 2 decimal places, and keeping the full value until the last step. The skill appears after every root, intersection or calculation in graphic display calculator interpretation.
How do you round correctly?
- Read the instruction. Decimal places count digits after the decimal point. Significant figures count from the first non-zero digit.
- Find the last digit you keep. Look at the digit after it.
- Round up if that digit is 5 or more, and leave the digit as it is if the next digit is 4 or less.
- Write trailing zeros where they matter. 16.0 to 3 significant figures shows the level of accuracy.
- Round only once, at the very end.
If there is no instruction, exam guidance usually expects a sensible level such as 3 significant figures for values that are not exact. Check the wording of each question.
Worked example
The positive root of x² − 2x − 4 = 0 is 1 + √5, and the calculator shows 3.236067977.
- 3 significant figures: the first three digits are 3, 2, 3. The next digit is 6, so round up: 3.24.
- 2 decimal places: the digits are 3.23 and the next digit is 6, so 3.24.
- 1 decimal place: 3.2 and the next digit is 3, so 3.2.
Notice that 3 significant figures and 2 decimal places agree here only because the number is between 1 and 10.
Why rounding early matters
Find (1 + √5)³ to 3 significant figures.
Correct: (1 + √5)³ = 1 + 3√5 + 15 + 5√5 = 16 + 8√5. With √5 = 2.2360680, 8√5 = 17.888544, so the value is 33.888544. To 3 significant figures: 33.9.
Early rounding: use 3.24 from the earlier step. 3.24² = 10.4976, and 10.4976 × 3.24 = 34.012224. To 3 significant figures that gives 34.0.
The answers differ in the third figure, because the small error in 3.24 was multiplied. The safe habit is to use the calculator’s stored answer, not a typed copy of a rounded number.
The mistake to watch for
Mistaken working: x = 3.24, so x³ = 34.0.
The first line is a fair rounding of the root, but the second line cannot be built on it. The correction is to keep the exact form or the full decimal, cube it, and round the result once. You can also write 1 + √5 in the working so the examiner sees the exact value before you round.
Check yourself
1. Give 0.0045678 to 2 significant figures.
Show answer
The first significant figure is 4, the second is 5, and the next digit is 6, which rounds up. The answer is 0.0046.
2. A calculator shows 15.996. Give it to 3 significant figures and to 1 decimal place.
Show answer
To 3 significant figures, the digits are 1, 5, 9 and the next digit is 9, so round up to 16.0. To 1 decimal place, 15.9 followed by 9 also rounds up to 16.0. Both answers are 16.0, and the zero must be written.
3. Round 12 345.6 to 3 significant figures.
Show answer
The first three digits are 1, 2, 3, and the next digit is 4, so the digit stays. The place value matters, so write 12 300, not 123.
Where this leads next
The next lesson shows how to write this down clearly in documenting a calculator-supported method. Test your rounding in the mixed practice set, and use the non-calculator working trainer to check exact arithmetic by hand.
Students who lose marks through accuracy rather than understanding often need a routine more than new content. A teacher in online one-to-one Mathematics tuition can build that routine with you.