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How to Round Numbers: Decimal Places and Significant Figures

Published October 3, 2026Written and reviewed by Mateuss M.

How to Round Numbers: Decimal Places and Significant Figures — illustration
In short: Look at the first digit you will drop: 5 or more rounds up, 4 or less rounds down. 3.14159 to 3 decimal places is 3.142.

Decimal places

Keep the stated number of digits after the point, and use the next digit to decide.

3.14159 to 3 d.p.
Answer3.142
Step-by-step working 3 steps
  1. 1
    The number
    3.14159
  2. 2
    Look at digit 4 after the point
    Next digit is 5  →  round up

    Digits 5 to 9 round up; 0 to 4 round down.

  3. 3
    Result
    3.14159 → 3.142

The 5 problem

1.005 to 2 d.p. is 1.01 by the school rule (half rounds up). Some programming languages show 1.00 because 1.005 cannot be stored exactly in binary — see why 0.1 + 0.2 is not 0.3.

Significant figures

Count from the first non-zero digit. 0.004567 to 3 s.f. keeps 4, 5, 6 and looks at the 7.

0.004567 to 3 s.f.
Answer0.00457
Step-by-step working 3 steps
  1. 1
    The number
    0.004567
  2. 2
    Find the first significant digit

    The first non-zero digit sits at the 10^-3 place, so 3 significant figures means rounding at the 10^-5 place.

  3. 3
    Result
    0.004567 → 0.00457

Nearest ten, hundred or other multiple

2750 to the nearest 100 is 2800; 13 to the nearest 5 is 15. Do all your rounding once, at the end — the rounding calculator shows the deciding digit.

Frequently asked questions

Do I round up or down on exactly 5?

The school convention rounds half up (away from zero). Some statistics software uses round-half-to-even.

Should I round in the middle of a calculation?

No. Keep full precision and round only the final answer.

Written and reviewed by Mateuss M.

Mateuss M. writes and reviews mathematical content for CalcSolver, focusing on online calculators, formulas, equations, and practical math tools. He reviews calculator functionality, calculation methods, formulas, examples, and explanations to help ensure that each tool is clear, useful, and easy to understand.

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