Significant Figures Calculator (2024)

Calculator Use

Add, subtract, multiply and divide with significant figures. Enter numbers, scientific notation or e notation and select the math operator. The calculator does the math and rounds the answer to the correct number of significant figures (sig figs).

You can use this calculator to double check your own calculations using significant figures.

Enter whole numbers, real numbers, scientific notation or e notation. Example inputs are 3500, 35.0056, 3.5 x 10^3 and 3.5e3.

Read more below for doing math with significant figures.

What are Significant Figures?

Significant figures are the digits of a number that are meaningful in terms of accuracy or precision. These digits provide information about how precise a calculation or measurement might be.

Significant Figures Rules

  1. Non-zero digits are always significant
  2. Zeros in between non-zero digits are always significant
  3. Leading zeros are never significant
  4. Trailing zeros are only significant if the number contains a decimal point

Examples of Significant Figures

How Many
Significant Figures?

Which Figures
are Significant?

81

2

8, 1

0.007

1

7

5200.38

6

5, 2, 0, 0, 3, 8

380.0

4

3, 8, 0, 0

78800

4

7, 8, 8, 0

78800.

5

7, 8, 8, 0, 0

Rules for Adding and Subtracting with Significant Figures

  1. Find the place position of the last significant digit in the least certain number
  2. Add and/or subtract the numbers in your calculation as you normally would
  3. Round the answer to the place position of least significance that you found in step 1

Example: Adding and Subtracting with Significant Figures

A step in your "Let's Make a Latte" chemistry lab assignment requires that you account for the volume of fluids in your latte.

You're starting with 7 oz. of milk, and your espresso machine uses 2.5 oz. of water to make a 2 oz. espresso shot -- the other 0.5 oz. remains in the espresso puck. Finally, your high tech milk steamer tells you how much water is used in the steaming process, out to 3 decimal places.

You make your espresso and see that you've pulled the perfect 2 oz. shot. You steam and froth your milk, and the steamer indicator says 0.063 oz. of water was used during the process. You need to add up 2 oz. espresso plus 7 oz. milk plus 0.063 oz. of steam. But because this is a chemistry lab assignment you have to do your math with significant figures.

Reviewing the rules for adding and subtracting with significant figures, find the place position of the last significant digit of your least certain number. Your milk and espresso are each one significant digit in volume, in the ones place.

Adding the volumes of fluid in your latte you have:

7 oz. milk + 2 oz. espresso + 0.063 oz. water = 9.063 oz.

9.063 oz. rounded to the ones place = 9 oz.

Although you have a volume of fluids that seems accurate to the thousandths, you have to round to the ones place because that is the least significant place value. So following the rules of addition with significant figures you report that your latte is 9 oz. in volume.

Rules for Multiplying and Dividing with Significant Figures

  1. For each number in your calculation find the number of significant figures
  2. Multiply and/or divide the numbers in your calculation as you normally would
  3. Round the answer to the fewest number of significant figures that you found in step 1

Example: Multiplying and Dividing with Significant Figures

A word problem on a physics test goes like this: Marine scientists have identified a unique whale who calls at 52 hertz. We know that sound travels in air at about 343 meters per second. Given that the sound of speed travels 4.3148688 times faster in water than in air, what is the wavelength of the 52 Hz whale call?

The formula for wavelength is:

\( \lambda = \dfrac{v}{f} \)

Where
\( \lambda \) = wavelength, in meters
\( v \) = velocity, at meters per second
\( f \) = frequency, at hertz

So wavelength equals velocity divided by frequency. For this physics problem you have to multiply velocity of the speed of sound in air by 4.3148688 to get the velocity of the speed of sound in water. Then divide this number by 52 Hz to get the wavelength of the sound wave.

  • \( \lambda = \dfrac{v}{f} \)

  • \( \lambda = \dfrac{343 \times 4.3148688}{52} \)

  • \( \lambda = \dfrac{1480}{52} \)

  • \( \lambda = 28.4615384 \) meters

Following the rules for doing multiplication and division with significant figures you should round your final answer to the fewest number of significant figures given your original numbers. In this case 52 has the fewest number of significant digits, so you should round the final answer to 2 sig figs.

28.4615384 meters rounded to 2 sig figs = 28 meters. So in water, one wavelength of a 52 Hz whale call is 28 meters long.

Note: Doing Math With Significant Figures

If you are entering a constant or exact value as you might find in a formula, be sure to include the proper number of significant figures.

For example, consider the formula for diameter of a circle, d = 2r, where diameter is twice the length of the radius. If you measure a radius of 2.35, multiply by 2 to find the diameter of the circle: 2 * 2.35 = 4.70

If you use this calculator for the calculation and you enter only "2" for the multiplier constant, the calculator will read the 2 as one significant figure. Your resulting calculation will be rounded from 4.70 to 5, which is clearly not the correct answer to the diameter calculation d=2r.

You can think of constants or exact values as having infinitely many significant figures, or at least as many significant figures as the the least precise number in your calculation. In this example you would want to enter 2.00 for the multiplier constant so that it has the same number of significant figures as the radius entry. The resulting answer would be 4.70 which has 3 significant figures.

Related Calculators

To learn more about rounding significant figures see our Rounding Significant Figures Calculator.

For more about rounding numbers in general see our Rounding Numbers Calculator.

To practice identifying significant figures in numbers see our Significant Figures Counter.

References

Significant Figures Calculator (2024)

FAQs

How do you find the number of significant figures? ›

We can identify the number of significant digits by counting all the values starting from the 1st non-zero digit located on the left. For example, 12.45 has four significant digits.

How do you round 0.00321609 to 3 significant figures? ›

(ii) To round the number 0.00321609 to 3 significant figures, we start counting from the leftmost nonzero digit, which is 3. The three digits following the 3 are 2, 1, and 6. Since the 2 is less than 5, we do not need to round up. Therefore, 0.00321609 rounded to 3 significant figures is 0.00322.

What is 0.9999 to 3 significant figures? ›

Answer and Explanation:

This means that 0.9999 rounded to three decimal places is 1.000.

How do you round 0.9968 to 2 significant figures? ›

The value given was 0.9968 which is to change into to 2 significant figures, if we count from the right hand, it will remain 0.99 which can be rounded up 1.00 because 9 is more that 5.

How many significant figures does 0.0100 have? ›

Just confirming, I know that 0.0100 would have 3 sigfigs due to trailing zeros, but would 1.00 have 3 as well?

How many significant figures does 0.00120 have? ›

We are given a number 0.00120, we have to find its significant figures. Since it has zero before the decimals, they will be insignificant, and after the decimal all are significant, so, 3 significant figures. Hence, 0.00120 have 3 significant digits.

What is 3.845 to 3 significant figures? ›

The number 3.845 rounded off to three significant figures becomes 3.84 since the preceding digit is even. On the other hand, the number 3.835 rounded off to three significant figures becomes 3.84 since the preceding digit is odd.

What is 9.99 to 1 significant figure? ›

fig. is 10. This may seem strange, because the number 10 only has 1 significant figure, but 9.99 rounded to 2 significant figures must be 10, because rounding it to 1 would be much too small.

Does 0.202 have 3 significant figures? ›

Zeroes at the right end after the decimal point are significant but if the zeroes are used for spacing for the decimal place, it is not considered significant (examples are the zeroes before and after the decimal point). From the given choices, (c) 0.202 g is expressed in 3 significant figures.

How do you round 78.56 to two significant figures? ›

Round 78.56 to two significant figures. The first significant figure is 7 7 7 and the second is 8 8 8. The next number to the right is 5 5 5, so we round up. Adding one to the 8 8 8 gives us 9 9 9 and therefore we have 79 79 79.

What is 0.9976 to 2 significant figures? ›

Final answer:

To round 0.9976 to 2 significant figures, you would get 1.0 x 10^0.

What is 0.0982 to 1 significant figure? ›

In this case, the digit to the right of the desired significant figure is 9, which is 5 or higher, so we round up. Therefore, 0.0982 to 1 significant figure is approximately 0.1.

References

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