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Significant Figures Calculator and Counter

Count significant figures, round numbers to a specified precision, convert scientific notation, and solve mathematical operations using significant-figure rules with clear explanations.

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이 도구는 브라우저에서 실행됩니다. 입력값, 파일, 생성된 값은 이 기기에 남습니다. 즐겨찾기와 최근 사용한 도구를 이용하더라도 로컬 저장소에는 도구 이름만 저장되며, 비밀번호나 문서, QR 내용은 절대 저장되지 않습니다. 자세한 내용은 개인정보처리방침을 확인하세요.

이 도구의 자세한 안내(사용법, 예시, 자주 묻는 질문)는 현재 영어로만 제공됩니다.

What this tool does

Count the significant figures in a written number, round it to a precision you choose, convert it to scientific notation, or add, subtract, multiply, and divide under the matching rule. The arithmetic stays in this browser tab. A whole number that ends in zero, such as 150, 80, or 1200, is left as a range instead of a single count.

How to use

  1. Choose Count significant figures, Round to significant figures, Convert to scientific notation, or an arithmetic operation.
  2. Enter the number. Decimals, a leading minus, and scientific notation such as 1.500e3 are accepted.
  3. For rounding, enter how many significant figures to keep. For arithmetic, enter each operand and mark a number exact only when it is a count or a defined conversion.
  4. Press Calculate. Read the result, the count or the limiting place, and the steps. Copy result writes the plain text.

Examples

  • 1.00 and 0.080

    1.00 has 3 significant figures. 0.08 has 1, and 0.080 has 2 because the last zero follows a decimal point.

  • 150, 80, and 1200

    150 can have 2 or 3 significant figures (1.5e2 or 1.50e2). 80 can have 1 or 2. 1200 can have 2, 3, or 4. The page does not pick one.

  • Rounding and arithmetic

    123.456 to 3 significant figures is 123. 999 to 2 is 1.0 × 10³. 12.11 + 0.3 is 12.4. 2.5 × 3.42 is 8.6. 15.0 ÷ 4.0 is 3.8.

Main features

  • Trailing zeros after a decimal point stay significant, so 1.00 has 3 and 0.080 has 2.
  • Trailing zeros in a whole number stay ambiguous, with a scientific-notation form for each possible count.
  • Rounding is half up and shows the precision you asked for, using scientific notation when a plain whole number would hide it.
  • Addition and subtraction use the least precise decimal place. Multiplication and division use the fewest significant figures.

How it works

The count follows the digits you typed, including zeros that the written form makes significant. Rounding keeps guard digits until the final half-up step. Addition and subtraction are not forced through the multiplication rule.

What the count uses

Nonzero digits are significant. Zeros between nonzero digits are significant, so 1005 has 4 and 10.01 has 4. Leading zeros are placeholders, so 0.08 has 1 and 0.00450 has 3.

Zeros after a decimal point that follow a nonzero digit are significant. 4.0, 2.0, 81.60, 1.00, and 1000.0 use that rule. A written zero such as 0 or 0.000 is counted as 1 significant figure. The decimal places in 0.000 still matter for addition.

The exponent in 1.5e3 or 1.500e3 does not change the coefficient. 1.5e3 has 2 significant figures. 1.500e3 has 4. 6.022e23 has 4. 3.00e-8 has 3.

Ambiguous whole numbers

150, 80, 1200, and 1000 end in zero and have no decimal point. The final zeros may be measured, or they may only hold a place. 150 is 2 or 3 significant figures. 80 is 1 or 2. 1200 is 2, 3, or 4. 1000 is 1 to 4.

Scientific notation removes the doubt. 1.200e3 has 4 significant figures. 1.20e3 has 3. 1.2e3 has 2. 1000.0 has 5 because the decimal point makes the zeros significant.

Rounding and the two operation rules

Half up means a first dropped digit of 5 or more increases the last kept digit by 1, away from zero. 1.2345 to 4 significant figures is 1.235. 1.25 to 2 is 1.3, and -1.25 to 2 is -1.3. 999 to 2 is 1.0 × 10³, copied as 1.0e3. 1200 to 4 is 1.200 × 10³.

12.11 + 0.3 is 12.4 because 0.3 stops at the tenths place. 2.5 × 3.42 is 8.6 because 2.5 has fewer significant figures. 15.0 ÷ 4.0 is 3.8. Division by zero is rejected. An exact number, such as a counted item or a defined conversion, does not limit the result.

Tips

  • Type 1.500e3 when you mean four significant figures. Typing 1500 leaves the count undecided.
  • Use the Percentage Calculator for a percent of a number. This page does not convert a result into a percent.

Limitations

Every typed number is treated as a measurement unless you mark it exact during arithmetic. The page cannot know whether the zero in 150 was measured. Precision above 50 significant figures is rejected, and exponents outside -9999 to 9999 are rejected. Results are the rules on this page, not a lab’s local rounding policy.

See the disclaimer for what these tools do not cover.

FAQ

Is the Significant Figures Calculator free?
Yes. You can count, round, convert, and calculate here without paying or creating an account.
How many significant figures does 150 have?
It cannot be determined from 150 alone. The count is 2 if the zero only holds the tens place (1.5 × 10²), or 3 if the zero was measured (1.50 × 10²).
Why does 1200 not get one count?
The trailing zeros have no decimal point, so they may or may not be significant. 1200 can have 2, 3, or 4 significant figures: 1.2e3, 1.20e3, or 1.200e3.
How do you round 999 to 2 significant figures?
999 to 2 significant figures is 1.0 × 10³. The plain whole number 1000 would hide that precision, so the result stays in scientific notation. The copyable form is 1.0e3.
What is 12.11 plus 0.3 with significant figures?
12.4. Addition uses the least precise decimal place. 0.3 is precise to the tenths place, and the exact sum 12.41 rounds half up to 12.4.
Are these numbers sent to a server?
No. The numbers are calculated in this browser tab. Tools Star Hub does not send them to a server or save them in local storage.

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