## Key Concepts and Summary

Quantities can be exact or measured. Measured quantities have an associated uncertainty that is represented by the number of significant figures in the measurement. The uncertainty of a calculated value depends on the uncertainties in the values used in the calculation and is reflected in how the value is rounded. Measured values can be accurate (close to the true value) and/or precise (showing little variation when measured repeatedly).

### Chemistry End of Chapter Exercises

- Express each of the following numbers in scientific notation with correct significant figures:

- 711.0
- 0.239
- 90743
- 134.2
- 0.05499
- 10000.0
- 0.000000738592

- Express each of the following numbers in exponential notation with correct significant figures:

- 704
- 0.03344
- 547.9
- 22086
- 1000.00
- 0.0000000651
- 0.007157

- Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:

- the number of eggs in a basket
- the mass of a dozen eggs
- the number of gallons of gasoline necessary to fill an automobile gas tank
- the number of cm in 2 m
- the mass of a textbook
- the time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h

- Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:

- the number of seconds in an hour
- the number of pages in this book
- the number of grams in your weight
- the number of grams in 3 kilograms
- the volume of water you drink in one day
- the distance from San Francisco to Kansas City

- How many significant figures are contained in each of the following measurements?

- 38.7 g
- 2 × 10
^{18}m - 3,486,002 kg
- 9.74150 × 10
^{-4}J - 0.0613 cm
^{3 } - 17.0 kg
- 0.01400 g/mL

- How many significant figures are contained in each of the following measurements?

- 53 cm
- 2.05 × 10
^{8}m - 86,002 J
- 9.740 × 10
^{4}m/s - 10.0613 m
^{3 } - 0.17 g/mL
- 0.88400 s

- The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.

- 0.0055 g active ingredients
- 12 tablets
- 3% hydrogen peroxide
- 5.5 ounces
- 473 mL
- 1.75% bismuth
- 0.001% phosphoric acid
- 99.80% inert ingredients

- Round off each of the following numbers to two significant figures:

- 0.436
- 9.000
- 27.2
- 135
- 1.497 × 10
^{-3 } - 0.445

- Round off each of the following numbers to two significant figures:

- 517
- 86.3
- 6.382 × 10
^{3 } - 5.0008
- 22.497
- 0.885

- Perform the following calculations and report each answer with the correct number of significant figures.

- 628 × 342
- (5.63 × 10
^{2}) × (7.4 × 10^{3}) - $\frac{28.0}{13.483}$
- 8119 × 0.000023
- 14.98 + 27,340 + 84.7593
- 42.7 + 0.259

- Perform the following calculations and report each answer with the correct number of significant figures.

- 62.8 × 34
- 0.147 + 0.0066 + 0.012
- 38 × 95 × 1.792
- 15 – 0.15 – 0.6155
- $8.78\times \left(\frac{0.0500}{0.478}\right)$
- 140 + 7.68 + 0.014
- 28.7 – 0.0483
- $\frac{\left(88.5-87.57\right)}{45.13}$

- Consider the results of the archery contest shown in this figure.

- Which archer is most precise?
- Which archer is most accurate?
- Who is both least precise and least accurate?

- Classify the following sets of measurements as accurate, precise, both, or neither.

- Checking for consistency in the weight of chocolate chip cookies: 17.27g, 13.05g, 19.46g, 16.92g
- Testing the volume of a batch of 25-mL pipettes: 27.02 mL, 26.99 mL, 26.97 mL, 27.01 mL
- Determining the purity of gold: 99.9999%, 99.9998%, 99.9998%, 99.9999%