Rounding Off Calculator (Decimal Places and Significant Figures)

Q: How do I round off to the nearest 10?

Look at the ones digit. If it is 5 or more, round up to the next ten; if it is 4 or less, round down. 45 → 50, 44 → 40.

Q: Is 2.5 rounded to 2 or 3?

In school maths, 3 — a 5 always rounds up (away from zero, so −2.5 → −3). Some computer programs use “round half to even” and give 2; this calculator uses the school rule and says so in the steps.

Q: How many significant figures are in 0.00450?

Three: 4, 5 and the last 0. The leading zeros only place the decimal point, but a trailing zero after the decimal point is significant.

Q: What is the difference between decimal places and significant figures?

Decimal places are counted after the decimal point; significant figures are counted from the first non-zero digit. 0.0457 has 4 decimal places but 3 significant figures.

Q: Why does my calculator give 2.67 for 2.675 to 2 decimal places?

Many calculators store 2.675 in binary as 2.67499999…, so they round down. This calculator works with the exact decimal digits you typed, so 2.675 → 2.68 as in your textbook.

Round any number to the nearest 10, 100, 1000 or lakh, to 1, 2 or more decimal places, or to a number of significant figures. The steps point out the rounding digit and the digit next to it, and apply the school rule: 5 or more, round up. It also counts the significant figures in your number — handy for Class 11 Physics and Chemistry.

Number

Round to the

Rounded

12300

Rule

Rounded down

Significant figures in your number

Leading zeros are not significant; every other digit is.

Step-by-step solution

Rounding digit (hundred place): 3. The next digit to the right is 4.
4 is less than 5 → round down: keep the rounding digit 3 and change the digits after it to 0.
12345.678 ≈ 12300

12345.678 rounded every way

Nearest 1,000	12000
Nearest 100	12300
Nearest 10	12350
Nearest whole number	12346
1 decimal place	12345.7
2 decimal places	12345.68
3 decimal places	12345.678
1 significant figure	10000
2 significant figures	12000
3 significant figures	12300

How to use the rounding off calculator

Type the number, e.g. 12,345.678 or 0.004572.
Choose how to round: to a place (nearest 10, 100, 1000…), to decimal places, or to significant figures.
Pick the place, the number of decimal places or the number of significant figures.
Read the rounded answer and the steps; the table below shows the same number rounded every common way.

Formulas

Rounding rule	`next digit 0–4 → round down; 5–9 → round up` School rule (round half up, away from zero): 2.5 → 3, −2.5 → −3.
Nearest 10 / 100 / 1000	`look at the ones / tens / hundreds digit`
Decimal places	`keep n digits after the point, look at digit n + 1`
Significant figures	`count from the first non-zero digit`
Scientific notation	`120000 (2 s.f.) = 1.2 × 10⁵`

Solved examples

Example 1: Round 4,672 to the nearest hundred.

Hundreds digit: 6; next digit (tens): 7
7 ≥ 5 → round up: 6 becomes 7, the rest become 0

Answer: 4,700

Example 2: Round 3.14159 to 2 decimal places.

Second decimal digit: 4; next digit: 1
1 < 5 → keep 4, drop the rest

Answer: 3.14

Example 3: Round 0.0045672 to 3 significant figures.

First significant figure: 4 (leading zeros do not count)
3 s.f. → 4, 5, 6; next digit 7 ≥ 5 → 6 becomes 7

Answer: 0.00457

Rounding vs estimation

Rounding replaces a number with a simpler one that is close to it: 4,672 ≈ 4,700. Estimation uses rounded numbers to check a calculation quickly — 4,672 × 19 is about 4,700 × 20 = 94,000 — which is a great way to catch mistakes in exams.

Always round only once, at the end. Rounding 2.449 to 2.45 and then to 2.5 gives the wrong answer; rounding 2.449 straight to 1 decimal place gives 2.4.

Significant figures rules

All non-zero digits are significant. Zeros between non-zero digits are significant (1002 has 4). Leading zeros are never significant (0.0045 has 2). Trailing zeros after a decimal point are significant (2.50 has 3) because they show the measurement was precise to that place. Trailing zeros in a whole number such as 1200 are ambiguous — write 1.2 × 10³ (2 s.f.) or 1.200 × 10³ (4 s.f.) to be clear.

Frequently asked questions

How do I round off to the nearest 10?