High School Chemistry : Scientific Notation and Significant Figures

Study concepts, example questions & explanations for High School Chemistry

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Example Questions

Example Question #51 : Measurements

Answer with the correct number of significant figures.

\displaystyle 1542 - 12.48 = ?

Possible Answers:

\displaystyle 1529.5

\displaystyle 1529.52

\displaystyle 1500

\displaystyle 2000

\displaystyle 1530

Correct answer:

\displaystyle 1530

Explanation:

Remember, when adding or subtracting, the answer uses the least number of decimal places. 1542 has the least number of decimal places (numbers after a decimal) because it has none. So the answer just needs to lack any decimal places.

Example Question #52 : Measurements

Answer with the correct number of significant figures.

\displaystyle (12.4) \cdot (32) \cdot (14.11) =?

Possible Answers:

\displaystyle 5599

\displaystyle 5.59 \cdot 10^3

\displaystyle 5.598 \cdot 10^4

\displaystyle 5598.848

\displaystyle 5600

Correct answer:

\displaystyle 5600

Explanation:

When multiplying or dividing, the answer uses the least number of significant figures of the given values. 12 had the least number of significant figures (2), so the answer must have 2 significant figures as well.

Example Question #53 : Measurements

Answer with the correct number of significant figures.

\displaystyle \frac{85.568}{45.51}=?

Possible Answers:

\displaystyle 1.8802

\displaystyle 1.880202153

\displaystyle 1.9

\displaystyle 1.88

\displaystyle 1.880

Correct answer:

\displaystyle 1.880

Explanation:

Remember: when multiply or dividing, the answer uses the least number of significant figures of the given values. Here, 45.51 has the least number of significant figures (4), which is why the answer must also have 4 significant figures.

Example Question #31 : Scientific Notation And Significant Figures

How many significant figures does 0.000500 have?

Possible Answers:

\displaystyle 3

\displaystyle 1

\displaystyle 7

\displaystyle 6

\displaystyle 4

Correct answer:

\displaystyle 3

Explanation:

When dealing with decimal numbers, zeros only count as long as there is a non-zero number somewhere before them. The first 4 zeros have no non-zero number before them, so they don't count as significant figures. The last 2 zeros have a 5 in front of them, so those zeros count as significant figures, and so does that 5; which gives us a total of 3 significant figures.

Example Question #62 : High School Chemistry

Which of the following numbers has 4 significant figures?

Possible Answers:

\displaystyle 2\cdot 10^3

\displaystyle 1340

\displaystyle 1001

\displaystyle 4\cdot 10^3

\displaystyle 8.11\cdot10^4

Correct answer:

\displaystyle 1001

Explanation:

For scientific notation, the exponent next to the ten has nothing to do with significant figures; it's the decimal number before it that determines the number of significant figures. Based on those decimal numbers, \displaystyle 2\cdot 10^3  and \displaystyle 4\cdot 10^3 each have one significant figure, and \displaystyle 8.11\cdot10^4 has three significant figures. When dealing with non-decimal numbers, zeros only count if they are in between two non-zero numbers. That means that 1,340 only has three significant figures, and 1,001 has 4 significant figures.

Example Question #21 : Using Significant Figures

Answer the following problem using the correct number of significant figures.

\displaystyle 130.5 \cdot 12 =?

Possible Answers:

\displaystyle 1566

\displaystyle 2000

\displaystyle 1600

\displaystyle 1570

\displaystyle 1560

Correct answer:

\displaystyle 1600

Explanation:

Whenever multiplying, the final answer will have the same number of significant figures as the number with the least least number of significant figures in the question. 130.5 has 4 significant figures and 12 has 2 significant figures, that means that our answer must have 2 significant figures. \displaystyle 130.5 \cdot 12 =1566, but that's 4 significant figures instead of 2. So we need to round this to 2 significant figures. Our answer to the correct number of significant figures is 1600.

Example Question #64 : Measurements

Answer the following using the correct number of significant figures.

\displaystyle 14.1 + 12 + 5.634 =?

Possible Answers:

\displaystyle 31.73

\displaystyle 31.7

\displaystyle 30

\displaystyle 32

\displaystyle 31.734

Correct answer:

\displaystyle 32

Explanation:

When adding numbers, the answer should use the the least number of decimal places of those in the question. 14.1 has one decimal place (one number behind the decimal), 12 has no decimal places, and 5.634 has 3 decimal places; this means that the answer must have no decimal places. \displaystyle 14.1 + 12 + 5.634 =31.734, this must be rounded to zero decimal places. Thus we round up to 32.

Example Question #63 : Measurements

You are doing an experiment and are measuring how the pressure changes of a gas in a container which you are changing the volume. You have the gas in a small cylinder that has mL markings. The pressure sensor has a high precision and can display pressures of \displaystyle \pm0.01\,kPa. You will be changing the volume by 1 mL for every data pair and recording the pressure. Your first data pair you write down is when you have a volume of \displaystyle 45.0\,mL which gives a pressure of \displaystyle 102.03\,kPa. If you write down \displaystyle 45.0\,mL for your volume, what is the appropriate number of significant figures to use for your first pressure measurement?

Possible Answers:

\displaystyle 100\,kPa

\displaystyle 102.0\,kPa

\displaystyle 102.03\,kPa

\displaystyle 102\,kPa

Correct answer:

\displaystyle 102\,kPa

Explanation:

Notice that the most precise you can get with your volume measurement is \displaystyle \pm0.1\,mL and your recorded value has 3 significant figures. You must take no more than 3 significant figures for your pressure measurement even if the device is more precise than this (which it is). Your recorded value must be

\displaystyle 102\,kPa

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