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

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## 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

What is stoichometry
what is atom
An indivisible part of an element
ngwuebo
the smallest particle of an element which is indivisible is called an atom
Aloaye
An atom is the smallest indivisible particle of an element that can take part in chemical reaction
Alieu
is carbonates soluble
what is the difference between light and electricity
What is atom? atom can be defined as the smallest particles
what is the difference between Anode and nodes?
What's the net equations for the three steps of dissociation of phosphoric acid?
what is chemistry
the study of matter
Reginald
what did the first law of thermodynamics say
energy can neither be created or distroyed it can only be transferred or converted from one form to another
Graham's law of Diffusion
what is melting vaporization
melting and boiling point explain in term of molecular motion and Brownian movement
Anieke
Scientific notation for 150.9433962
what is aromaticity
aromaticity is a conjugated pi system specific to organic rings like benzene, which have an odd number of electron pairs within the system that allows for exceptional molecular stability
Pookieman
what is caustic soda
sodium hydroxide (NaOH)
Kamaluddeen
what is distilled water
Rihanat
is simply means a condensed water vapour
Kamaluddeen
a hydrocarbon contains 7.7 percent by mass of hydrogen and 92.3 percent by mass of carbon
how many types of covalent r there
how many covalent bond r there
JArim
they are three 3
TYPES OF COVALENT BOND-POLAR BOND-NON POLAR BOND-DOUBLE BOND-TRIPPLE BOND. There are three types of covalent bond depending upon the number of shared electron pairs. A covalent bond formed by the mutual sharing of one electron pair between two atoms is called a "Single Covalent bond.
Usman