**Practice Problems on Working with
Significant Figures**

*It is assumed that you already know the rules on working with
significant figures. If you don’t, you
should review the “Tutorials on Significant Figures” accessed from my Homepage.*

**Quick Reminder**:

- If
you are adding or subtracting, the answer has the same # of
as that of the least given.__decimal places__ - If
you are multiplying or dividing, the answer has the same # of
as that of the least given.__significant figures__ - If
you are doing a mix of addition, subtraction, multiplication, and
division, then you need to be REALLY careful! You need to do the addition and
subtraction
, looking at decimal places and writing down the answer to the correct__first__before doing the multiplication and division, but this time, noting the correct__decimal places__(If you don’t know what I mean, you should go to the “Tutorials on Significant Figures” and review Step 4 “Keeping Track of Significant Figures During Calculations.” If you are working with the printed handout from class, this is on page 5..__significant figures__

Before you begin, remind yourself that these are not simple arithmetic problems. The point of this exercise is for you to practice WATCHING YOUR SIGNIFICANT FIGURES!

*Answers are provided at the bottom.
Be sure to WRITE DOWN YOUR ANSWERS before you look at the correct
answers provided.*

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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. 1.8x10^{3} (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 1.8x10^{3}.)

4. 1.4 x 10^{3} (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 1.4x10^{3}.)

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