9.1 Significant figures in calculations

The results of measurements are often used in calculations, and we then need to know how many figures to quote in the final answer. As a rule of thumb, when multiplying and dividing numbers, the number of significant figures in the result should be the same as in the measurement with the fewest significant figures. For example, if the length of a flower bed is 4.5 m and its width is 1.09 m, then the calculated area is 4.5 m multiplication 1.09 m = 4.905 m2. However, since the length of 4.5 m is measured only to two significant figures, we are only justified in quoting the area to two significant figures, so we would round the calculated value to 4.9 m2.

You may have a problem with multiple parts where you are asked to carry forward the answer from the first part and carry out further calculations. Always use the unrounded answer from the first part into the calculation for the second part and then round your answer.

For example, suppose we were asked to increase the area of the flower bed above by 0.048 m2. If we used the previously rounded figure of 4.9 m2 then the total area is 4.9 m2 + 0.048 m2 = 4.948 m2. This answer should still only be given to two significant figures, so it would be rounded down to 4.9 m2. However the correct method is to use the unrounded answer of 4.905 m2 from the first part. The total area is now 4.905 m2 + 0.048 m2 = 4.953 m2. Quoting this to two significant figures means that it should be rounded up to 5.0 m2.

Question 9.4

Do the following calculations and express your answers to the appropriate number of significant figures:

    • a.0.43 m division 1.2 s

  • multiline equation row 1 0.43 m prefix division of 1.2 s equals 0.358 times 333 times 333 times three times m s super negative one row 2 Blank equals 0.36 times m s super negative one to two significant figures

    Note: If you were using this result in subsequent calculations you should use the unrounded value, or a value quoted to at least one additional digit.

    • b.2.373 m multiplication 3.6 m

  • multiline equation row 1 2.373 m prefix multiplication of 3.6 m equals 8.542 times eight times m super two row 2 Blank equals 8.5 times m super two to two significant figures

    Note: If you were using this result in subsequent calculations you should use the unrounded value, or a value quoted to at least one additional digit.

    • c.6 342 kg division 2.42 m3

  • multiline equation row 1 six times 342 kg prefix division of 2.42 times m super three equals two times 620.661 times 157 times kg m super negative three row 2 Blank equals 2.62 multiplication 10 cubed times kg m super negative three in scientific notation and row 3 Blank to three significant figures

    Note: If you were using this result in subsequent calculations you should use the unrounded value, or a value quoted to at least one additional digit.

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9 Significant figures
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10 Reading data from tables