Sig Fig Calculator

Sig fig calculator at a glance#

What are significant figures?#

Significant figures, often called sig figs, are the digits in a number that provide information about the precision of the measurement. You count from the first nonzero digit to the last digit that was actually measured. Zeros that only indicate the location of the decimal point do not count.

How do you count significant figures?#

Every nonzero digit is counted, as well as every zero that appears between two nonzero digits. Leading zeros are never counted. Trailing zeros count when there is a decimal point but are ambiguous without one. If you type a number into the calculator above, it will return the count and list each significant digit.

How many sig figs are in 50.0?#

50.0 has 3 significant figures. The final zero is to the right of the decimal point, which means it was measured and counts. The zero before the decimal point is between two significant digits, so it also counts. When written as 50 with no decimal point, the value has 1 significant figure by standard convention.

What significant figures tell you#

The precision of a measurement is limited by the tool used to take it. For example, if a lab balance reads a sample at 0.04050 grams, the digits 4, 0, 5, and 0 come from the balance, with the final zero indicating precision to the hundred-thousandth of a gram. The two zeros in front only serve to locate the decimal point. If you express the same mass as 40.50 milligrams, those zeros vanish, but the measured digits remain unchanged. Either way, the reading has 4 significant figures. The rules below all come back to 0.04050.

The OpenStax Chemistry 2e textbook states the counting rule: begin with the first nonzero digit on the left, then count it along with every digit to its right. The exception is a whole number ending in zeros, which is addressed below.

The rules for counting significant figures#

Every digit falls under one of these rules.

• Nonzero digits are always counted. 4.5 has 2 significant figures.
• Captive zeros, which are zeros situated between nonzero digits, are always included. 4006 has 4.
• Leading zeros, or zeros that appear before the first nonzero digit, are not counted. 0.045 has 2.
• Trailing zeros located to the right of the decimal point are counted. 0.50 has 2, and 350.00 has 5.
• Trailing zeros in a whole number without a decimal point are ambiguous. 400 could have 1, 2, or 3. OpenStax recommends considering them not significant when the written number is all that's available, and the calculator above follows this advice, so 400 gives 1.

In the case of 0.04050, the two leading zeros are not counted. The 4 and the 5 are counted, with the zero between them being captive and thus counted, and the final zero, located to the right of the decimal point, is also counted. That makes 4 significant figures: 4, 0, 5, and 0.

How to count sig figs step by step#

1. Identify the first nonzero digit. Everything preceding it is a leading zero and is not counted.
2. Include that digit and every following digit, counting zeros as well.
3. If the number lacks a decimal point and ends with zeros, stop counting at the last nonzero digit unless those zeros were known to be measured.
4. For scientific notation, consider only the digits before the times sign. The power of 10 does not contribute additional figures.

For 0.04050, the first nonzero digit is 4. Counting 4, 0, 5, and 0 gives 4 significant figures. Type 0.04050 into the calculator to confirm, and it lists the same four digits.

Trailing zeros and the decimal point#

Most counting mistakes involve trailing zeros, and the key question is whether there's a decimal point.

• With a number like 50, you have 1 significant figure. Without a decimal point, the zero may just be a placeholder.
• The number 50. has 2 significant figures. When a decimal point is present after the zero, it indicates that the ones place was measured.
• For 50.0, there are 3 significant figures. The zero following the decimal point was measured, making the zero before it significant too.
• In the case of 50.00, it has 4 significant figures.

This logic extends to larger numbers. For instance, 1200 has 2 significant figures by the calculator's convention. Meanwhile, 1200. has 4 significant figures, and 1200.0 has 5. If a whole number is measured to the ones place, adding a trailing decimal point or using scientific notation helps avoid any confusion.

Significant figures in scientific notation#

Scientific notation clears up any ambiguity. A number is expressed as a coefficient between 1 and 10 multiplied by a power of 10, where each digit in the coefficient is significant. For example, 1.2 × 10³ has 2 significant figures, 1.20 × 10³ has 3, and 1.200 × 10³ has 4, despite all of them being equal to 1200. The worked example becomes 4.050 × 10⁻² grams, still 4 significant figures.

The calculator can handle scientific notation input using the letter x, as in 4.050 x 10^-2, and E notation, as seen in 4.050e-2. It counts the digits in the coefficient while ignoring the exponent. To switch a number between standard and scientific notation, use the scientific notation calculator.

Sig figs in calculations#

Calculated answers should match the precision of their measurements. For multiplication or division, round the answer to the lowest number of significant figures from the inputs. For addition or subtraction, round to the fewest decimal places. This calculator determines the significant figures in a single number. For rounding a result to a specific number of figures, use the significant figures calculator, whose page works through both rules with examples.

Where sig figs matter#

Counting sig figs tells you how precise a recorded number is. A mass written as 0.04050 g was recorded to the hundred-thousandth of a gram, while 0.0405 g stops at the ten-thousandth. When you read a marked scale yourself, write down every digit you are sure of plus one estimated digit. For example, a ruler marked in millimeters allows recording a length such as 12.35 cm, with the last digit estimated between two marks, which is 4 significant figures (approximately 4.86 inches).

How many sig figs: common numbers#

These are numbers people often check. Each count follows the rules above and matches the calculator's output.

Sources#

• OpenStax, Chemistry 2e, section 1.5: Measurement Uncertainty, Accuracy, and Precision
• Texas Instruments, TI-84 Plus CE guidebook: FLOAT 0 1 2 3 4 5 6 7 8 9 (decimal mode setting)

Frequently asked questions#

Do trailing zeros count as significant figures?#

Trailing zeros do count when the number has a decimal point, so 0.00990 has 3 and 350.00 has 5. In whole numbers without a decimal point, like 400, trailing zeros become ambiguous, and the calculator treats them as placeholders. To indicate they were measured, either add a decimal point or use scientific notation.

How many sig figs are in 0.50?#

0.50 has 2 significant figures. The zero in front of the decimal point is considered a leading zero and doesn't count. The 5 counts as a significant figure, and the final zero is also counted because it is to the right of the decimal point.

How many sig figs does 50 have?#

By the usual convention, 50 has 1 significant figure because a trailing zero with no decimal point typically only holds the place. If the zero was measured, write 50. for 2 significant figures or 50.0 for 3.

Do leading zeros count as significant figures?#

Leading zeros do not count as significant figures. They only indicate the position of the decimal point, so 0.045 has 2 significant figures and 0.00413 has 3. Changing units makes this clear: 0.045 meters converts to 4.5 cm, and the zeros disappear without any change in the measurement.

How do you count sig figs in scientific notation?#

Count the digits in the coefficient only. 6.022 × 10²³ has 4 significant figures and 4.50 × 10⁻³ has 3. The exponent determines the size of the number, not its precision.

Can a graphing calculator count significant figures?#

Not on its own. On a TI-84, the MODE screen offers a decimal setting from 0 to 9 that defines how many digits appear to the right of the decimal point. Texas Instruments says this applies in Normal, Sci, and Eng notation. In Sci notation with 2 decimal places, every answer shows 3 significant figures. That rounds the display. To count the figures in a number you already have, use the calculator above.

Do exact numbers have significant figures?#

Exact numbers have unlimited significant figures. Counted items, like 24 students in a class, and defined conversions, such as 1 inch = 2.54 cm, carry no measurement uncertainty. They never limit the precision of a result.