Practice Problems on Working with Significant Figures



Practice Problems on Working with Significant Figures

Quick Reminder:

• If you are adding or subtracting, the answer has the same # of decimal places as that of the least given.

• If you are multiplying or dividing, the answer has the same # of significant figures as that of the least given.

• If you are doing a mix of addition, subtraction, multiplication, and division, then you need to be REALLY careful!

o You need to do the addition and subtraction first, looking at decimal places and writing down the answer to the correct decimal places before doing the multiplication and division, but this time, noting the correct significant figures.

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9. The following are placed in a beaker weighing 39.457 g

2.689 g of NaCl, 1.26 g of sand and 5.0 g water

What is the final mass of the beaker?

10. If the beaker containing a sample of alcohol weighs 49.8767 g and

the empty beaker weighs 49.214 g, what is the weight of the alcohol?

Answers:

1) 40.9 (This is an addition problem. The limiting factor is 1.3, with one decimal place.)

2) 2 (This is a subtraction problem. The limiting factor is 193, with NO decimal place.)

3) 1.8x103 (This is an addition problem. The limiting factor is 1200, which has “ambiguous zeroes”

which are assumed to be not significant. We are therefore limited to the hundreds place.

The answer is 1800 but to eliminate the ambiguity of the tailing zeroes, it MUST be

expressed in scientific notation, hence 1.8x103.)

4) 1.4 x 103 (900 and 500 have ambiguous zeroes that are assumed to be not significant. The ans is

limited to the hundreds place. It is 1400 with ambiguous zeroes, so it must be expressed

in scientific notation, hence 1.4x103.)

5) 5.4 (Both numbers in the question has one decimal place, so ans should have one decimal place.)

6) 18 (This involves only multiplication and division. The limiting factor is 2.9 with 2 sig. fig.,

so the answer should have 2 sig. fig.. Note there is no reason to express it in scientific

notation.)

7) 1.4 (This has a mix of subtraction and division, with different rules, so you must do them

separately. 23.5 – 21.3 = 2.2 (with one decimal place) and then dividing 2.2 by 1.58, the

answer is 1.4 with 2 significant figures.)

8) 0.396

9) 48.4 g

10) 0.663 g

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