Rounding and significant figures calculator
Type a number and choose how you want it rounded — to significant figures or decimal places — and this tool shows the digit you look at, the rounded value, and the error bounds that come with it. Error bounds appear in almost every higher-tier accuracy question, so they are calculated for you automatically.
Enter a number and choose the accuracy
12.5
Error bounds: 12.45 ≤ x < 12.55
Lower bound: 12.45 · Upper bound: 12.55
Working
- The first significant figure is in the 10 column, so 3 s.f. rounds to the nearest 0.1.
- Look at the next digit: 5 or more rounds up, otherwise round down.
- 12.4567 → 12.5
- Error bounds = rounded value ± half of 0.1 = 12.5 ± 0.05
The method behind it
- Significant figures start at the first non-zero digit; decimal places start after the point.
- Look at the next digit: 5 or more rounds up, otherwise round down.
- Error bounds = rounded value ± half the place value being rounded to.
How to use this tool
1. Enter the number
Any decimal or negative number works. Very large and very small values are handled without switching to standard form.
2. Pick the accuracy
Choose significant figures or decimal places and set how many you need.
3. Read the bounds
The lower bound and upper bound show the interval the true value must lie in, written as lower ≤ x < upper.
Frequently asked questions
What counts as a significant figure?
Start counting from the first non-zero digit. Zeros between digits are significant, and trailing zeros after a decimal point are significant. Leading zeros, as in 0.0043, never count.
How do you round to 3 significant figures?
Find the third significant digit, then look at the next digit. If it is 5 or more, round the third digit up; otherwise leave it. Fill any gaps back to the decimal point with zeros.
What are upper and lower bounds?
They are the limits of the interval the original value could have come from. A length given as 12.4 cm to 1 decimal place has a lower bound of 12.35 cm and an upper bound of 12.45 cm.
Why is the upper bound written with a < sign?
Because a value exactly equal to the upper bound would round up to the next value instead. So the correct statement is 12.35 ≤ x < 12.45.
Practise this properly, not just once
A solver gives you the answer; exam marks come from the working. MathsGradeUp pairs exam-board questions with step-by-step feedback and revision notes on the exact topics you keep dropping marks on.