# 1.6 Mathematical treatment of measurement results  (Page 5/9)

 Page 5 / 9

## Key concepts and summary

Measurements are made using a variety of units. It is often useful or necessary to convert a measured quantity from one unit into another. These conversions are accomplished using unit conversion factors, which are derived by simple applications of a mathematical approach called the factor-label method or dimensional analysis. This strategy is also employed to calculate sought quantities using measured quantities and appropriate mathematical relations.

## Key equations

• ${T}_{\text{°C}}=\phantom{\rule{0.2em}{0ex}}\frac{5}{9}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{T}_{\text{°F}}-32$
• ${T}_{\text{°F}}=\phantom{\rule{0.2em}{0ex}}\frac{9}{5}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{T}_{\text{°C}}+32$
• ${T}_{\text{K}}=\text{°C}+273.15$
• ${T}_{\text{°C}}=\text{K}-273.15$

## Chemistry end of chapter exercises

Write conversion factors (as ratios) for the number of:

(a) yards in 1 meter

(b) liters in 1 liquid quart

(c) pounds in 1 kilogram

(a) $\frac{\text{1.0936 yd}}{\text{1 m}}$ ; (b) $\frac{\text{0.94635 L}}{\text{1 qt}}$ ; (c) $\frac{\text{2.2046 lb}}{\text{1 kg}}$

Write conversion factors (as ratios) for the number of:

(a) kilometers in 1 mile

(b) liters in 1 cubic foot

(c) grams in 1 ounce

The label on a soft drink bottle gives the volume in two units: 2.0 L and 67.6 fl oz. Use this information to derive a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?

$\begin{array}{c}\frac{\text{2.0 L}}{\text{67.6 fl oz}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{\text{0.030 L}}{\text{1 fl oz}}\end{array}$
Only two significant figures are justified.

The label on a box of cereal gives the mass of cereal in two units: 978 grams and 34.5 oz. Use this information to find a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?

Soccer is played with a round ball having a circumference between 27 and 28 in. and a weight between 14 and 16 oz. What are these specifications in units of centimeters and grams?

68–71 cm; 400–450 g

A woman's basketball has a circumference between 28.5 and 29.0 inches and a maximum weight of 20 ounces (two significant figures). What are these specifications in units of centimeters and grams?

How many milliliters of a soft drink are contained in a 12.0-oz can?

355 mL

A barrel of oil is exactly 42 gal. How many liters of oil are in a barrel?

The diameter of a red blood cell is about 3 $×$ 10 −4 in. What is its diameter in centimeters?

8 $×$ 10 −4 cm

The distance between the centers of the two oxygen atoms in an oxygen molecule is 1.21 $×$ 10 −8 cm. What is this distance in inches?

Is a 197-lb weight lifter light enough to compete in a class limited to those weighing 90 kg or less?

yes; weight = 89.4 kg

A very good 197-lb weight lifter lifted 192 kg in a move called the clean and jerk. What was the mass of the weight lifted in pounds?

Many medical laboratory tests are run using 5.0 μL blood serum. What is this volume in milliliters?

5.0 $×$ 10 −3 mL

If an aspirin tablet contains 325 mg aspirin, how many grams of aspirin does it contain?

Use scientific (exponential) notation to express the following quantities in terms of the SI base units in [link] :

(a) 0.13 g

(b) 232 Gg

(c) 5.23 pm

(d) 86.3 mg

(e) 37.6 cm

(f) 54 μm

(g) 1 Ts

(h) 27 ps

(i) 0.15 mK

(a) 1.3 $×$ 10 −4 kg; (b) 2.32 $×$ 10 8 kg; (c) 5.23 $×$ 10 −12 m; (d) 8.63 $×$ 10 −5 kg; (e) 3.76 $×$ 10 −1 m; (f) 5.4 $×$ 10 −5 m; (g) 1 $×$ 10 12 s; (h) 2.7 $×$ 10 −11 s; (i) 1.5 $×$ 10 −4 K

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