Chapter 2 - Measured numbers, sig figs and metric system

Question 1

Measured numbers

Answer 1

are the numbers obtained when you measure a quantity such as your height, weight, or temperature.

Question 2

Significant Figures

Answer 2

The significant figures (SFs) are all the digits including the estimated digit.
Significant figures are
•used to represent the amount of error associated with a measurement
•all nonzero digits and zeros between digits
•not zeros that act as placeholders before digits
•zeros at the end of a decimal number

Non-zero digits are always significant
Any zeros between two significant digits are significant
A final zero or trailing zeros in the decimal portion ONLY are significant
Example: .500 or .632000 the zeros are significant

             .006  or .000968 the zeros are NOT significant

Question 3

Scientific Notation and sig fig

Answer 3

Zeros at the end of large standard numbers without adecimal point are not significant.
• 400 000 g is written with one SF as 4 × 105 g• 850 000 m is written with two SF as 8.5 × 105 m

Zeros at the beginning of a decimal number are used as placeholders and are not significant.
• 0.000 4 s is written with one SF as 4 × 10−4 s• 0.000 0046 g is written with two SF as 4.6 × 10−6 g

Question 4

Identify the numbers below as measured or exact, and give the number of significant figures in each measured number.
A. 3 coins
B. The diameter of a circle is 7.902 cm.
C. 60 min = 1 h

Answer 4

A.3 coins is a counting number and therefore is an exact number.
B. The diameter of a circle is 7.902 cm. This is a measured number and the zero is significant, so it contains four SF.
C.60 min = 1 h is exact by definition.

Question 5

Metric and SI prefixes

Answer 5

Name Symbol Factor Name

larger quantities
or whole units	yotta	Y	1024	Septillion
zetta	Z	1021	Sextillion
exa	E	1018	Quintillion
peta	P	1015	Quadrillion
tera
Example: terahertz	T	1012	Trillion
giga
Example: gigawatt	G	109	Billion
mega	M	106	Million
kilo
Example: kiloliter	k	103	Thousand
hecto
Example: hectare	h	102	Hundred
deka
Example: dekameter	da	101	Ten
 	 	 	100	One
smaller quantities
or sub units

 	deci
Example: decimeter	d	10-1	Tenth
centi
Example: centigram	c	10-2	Hundredth
milli
Example: milliliter	m	10-3	Thousandth
micro
Example: microgram	μ	10-6	Millionth
nano
Example: nanometer	n	10-9	Billionth
pico
Example: picogram	p	10-12	Trillionth
femto
Example: femtosecond	f	10-15	Quadrillionth
atto	a	10-18	Quintillionth
zepto
Example: zeptosecond	z	10-21	Sextillionth
yocto
Example: yoctosecond	y	10-24	Septillionth

Question 6

cubic centimeter

Answer 6

The cubic centimeter (abbreviated as cm3 or cc) is the volume of a cube whose dimensions are 1 cm on each side. A cubic centimeter has the same volume as a milliliter, and the units are often used interchangeably. 1 cm3 = 1 cc = 1 mL

Question 7

Conversion Factors in a Problem

Answer 7

A conversion factor
•may be stated within a problem that applies only to that problem
•is written for that problem only Example: The car was traveling at 85 km/h.

85km=1h
85km/1h and 1h/85km

Question 8

Problem Solving Using Unit Conversions

Example: If a person weighs 164 lb, what is the body mass in kilograms?

Answer 8

STEP 1 State the given and needed quantities.
STEP 2 Write a plan to convert the given unit to the needed unit. (pounds. kilograms)
ANALYZE the problem:
GIVEN (164lb) NEED(Kilograms)

Question 9

Example: If a person weighs 164 lb, what is the body mass in kilograms?

Answer 9

STEP 3 State the equalities and conversion factors.
1kg=2.20lb

STEP 4 Set up the problem to cancel units and calculate the answer.
164lb x 1kg/2.20lb = 74.5kg
because lbs are canceled.

Question 10

A rattlesnake is 2.44 m long. How many centimeters long is the snake?

Answer 10

244cm (3SF)

Question 11

How many minutes are in 1.4 days?

Answer 11

2.0 x 10 to the 3 min

Question 12

If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7.5 kilometers?

Answer 12

120 min (2SF)

Question 13

Density

Answer 13

Density compares the mass of an object to its volume.

D=m/v
Density = mass over volume

Question 14

An unknown liquid has a density of 1.32 g/mL. What is the volume of a 14.7-g sample of the liquid?

Answer 14

11.1mL liquid

Question 15

What is the density (g/cm3) of a 48.0-g sample of a metal if the level of water in a graduated cylinder rises from 25.0 mL to 33.0 mL after the metal is added?

Answer 15

6.0g/mL

Question 16

Example: John took 2.0 teaspoons (tsp) of cough syrup for a cough. If the syrup had a density of 1.20 g/mL and there is 5.0 mL in 1 tsp, what was the mass, in grams, of the cough syrup?

Answer 16

12 g syrup

Question 17

An unknown liquid has a density of 1.32 g/mL. What is the volume of a 14.7-g sample of the liquid?

Answer 17

11.1mL

Question 18

A doctor’s order prescribed a dosage of 0.150 mg of Synthroid. If tablets in stock contain 75 mcg of Synthroid, how many tablets are required to provide the prescribed medication?

Answer 18

2 tablets

Question 19

1) 52.30 mL =_____dL

Answer 19

0.5230dL

Question 20

4.90 kg = _____dg

Answer 20

4.90 x 10 to the 4dg

Question 21

462.9 m3 = ____cm3

Answer 21

4.629 x 10 to the -10 cm cubed (3)

Question 22

Calculate how far light travels in centimeters after one nanosecond. The speed of light is 3.00 x 108 m/s. (The distance light travels in a nanosecond really matters in computing and the size of the processor! )

Answer 22

3.00 x 10 to the 1 cm/ns

Question 23

Stavudine is an antiviral drug that has been tested as a treatment for AIDS. The daily recommended dosage of stavudine is 1.0 mg/kg of body weight. How many grams of this drug should be administered to a 150 lb patient?

Answer 23

0.068 g drugs

Question 24

The density of osmium is reported by one source to be 22610 kg/m3. What is this density in g/cm3? What is the mass of a block of osmium measuring 10.0 cm x 8.0 cm x 9.0 cm?

Answer 24

1.6 x 10 to the 4g

Question 25

The volume of blood plasma in adults is 3.1 L. Its density is 1.03 g/cm3. Approximately how many pounds of blood plasma are there in your body?

Answer 25

7lbs

Question 26

A 15-gallon tank is completely filled with gasoline. How many pounds of gasoline is this? Use 0.71 g/mL for the density of gasoline

Answer 26

89lbs

Question 27

Blood concentrations of the hormone cortisol in humans fluctuate within a 24-hour cycle as shown on the graph. What is the concentration of plasma cortisol when it peaks at 9 am?
given 18 ug/dL

Answer 27

to ug/L:
180ug/L

to g/dL
1.8 x 10 to the negative 5 g/dL

to mg/mL
1.8 x 10 to the negative 4mg/mL

Question 28

When counting significant figures, all nonzero digits are significant. A zero is significant if it meets certain criteria:
Zeros between nonzero digits are significant (e.g., 11.005 g ).
Zeros at the end of a decimal number are significant (e.g., 60.0 ∘C ).
Zeros in the coefficient of a number in scientific notation are significant (e.g., 1.80×104 kg ).
Otherwise, you can assume the zero is not significant.

Answer 28

TRUE

Question 29

A nurse practitioner prepares an injection of promethazine, an antihistamine used to treat allergic rhinitis. If the stock bottle is labeled 20. mg/mL and the order is a dose of 11.5 mg , how many milliliters will the nurse draw up in the syringe?

Answer 29

The stock bottle concentration, in milligrams per milliliter, is used as a conversion factor to calculate the volume (in milliliters) that contains 11.5 mg of the medication. The conversion factor is inverted to allow the units of milligrams to cancel, as shown here:

11. 5mg×1 mL20. mg
12. 58mL

Question 30

You are to give ampicillin, with a recommended dose of 45 mg/kg , to a child with a mass of 22 kg . If stock on hand is 250 mg/capsule, how many capsules should be given?
Express the number of capsules as an integer.

Answer 30

Based on the child’s weight, the required dose is 990 mg . The amount of ampicillin in each capsule is used as a conversion factor to calculate the number of capsules that will deliver that dose.

4capsule(s)

Question 31

Aluminum has a density of 2.70 g/mL. Calculate the mass (in grams) of a piece of aluminum having a volume of 339 mL .
Express your answer to three significant figures.

Answer 31

A piece of aluminum with a volume of 339 mL will have a mass of 915 g . This can be calculated by multiplying 339 mL by the conversion factor of 2.70gmL .

mass =915g

Question 32

Converting between SI units

Answer 32

Factor	Name	Symbol
106  	mega	M
103  	kilo   	k
102  	hector	h
101	        deka	da
10−1	        deci  	d
10−2	centi	c
10−3	milli  	m
10−6	micro	μ

Question 33

Iron has a density of 7.86 g/cm3. Calculate the volume (in dL) of a piece of iron having a mass of 3.52 kg . Note that the density is provided in different units of volume and mass than the desired units of volume (dL) and the given units of mass (kg). You will need to express the density in kg/dL (1 cm3 = 1 mL) before calculating the volume for the piece of iron.
Express your answer to three significant figures.

Answer 33

The first step is to convert the given density, 7.86 g/cm3 , into the desired units of kg/dL . This is effectively using three conversion factors, one for converting grams to kilograms, one for converting cm3 to mL , and then one for converting to dL , to create a density conversion factor with the units needed to properly cancel the given mass value.
7.86 g1 cm3 × 1 kg1000 g × 1 cm31 mL × 100 mL1 dL = 0.786 kg/dL

Then, simply divide the given mass by the density to arrive at the correct answer of 4.48 dL :
3.52kg0.786 kg/dL = 4.48dL

volume =4.48dL

Question 34

A 5.23 g sample of a metal occupies 0.27 mL. Identify the density of the metal.

Answer 34

19 g/mL

Question 35

0.39 lb to grams

Express your answer using two significant figures.

Answer 35

180g

In 1 lb , there are 454 grams. This is written as a fraction so that the unwanted unit of lb cancels out and the wanted unit of gram remains.

number of grams=0.39lb×454g1lb=180 g

Question 36

14.6 in. to centimeters

Express your answer using three significant figures.

Answer 36

37.1cm

In 1 in , there are 2.54 cm . This is written as a fraction with in in the denominator and cm in the numerator so that the unwanted unit of in cancels out and the wanted unit of centimeter remains.

number of centimeters=14.6in×2.54cm1in

Question 37

A doctor orders 6.5 mL of phenobarbital elixir. If the phenobarbital elixir is available as 60. mg per 7.5 mL, how many milligrams is given to the patient?
Express your answer to two significant figures and include the appropriate units.

Answer 37

52 mg

According to the question,

In 7.5 mL,

→ Phenobarbital elixir is found = 60 mg

then,

In 1 mL,

→ Phenobarbital elixir is found = 60/7.5

or,

                                           = 8mg

In 6.5 mL,

→ Phenobarbital elixir is found,

= 60/7.5 x 6.5mL
= 52mg

Question 38

The water level in a graduated cylinder is initially at 215 mL and rises to 275 mL after a piece of lead is submerged. What is the mass, in grams, of the lead (D=11.3g/mL)?
Express your answer to two significant figures and include the appropriate units.

Answer 38

6.8×10 to the 2 g

When the lead is completely submerged in water, it displaces a volume of water equal to its own volume. After subtracting the initial volume from the final volume in the graduated cylinder, this volume is converted into grams of lead using the density as a conversion factor.

mass of lead = (Vfinal−Vinitial)×density
=(275mL−215mL)×11.3gmL
=60.mL×11.3gmL
=6.8×10 to the 2g

Question 39

A nurse practitioner orders Medrol to be given 1.2 mg/kg of body weight. Medrol is an anti-inflammatory administered as an intramuscular injection. If a child weighs 72.0 lb and the available stock of Medrol is 20. mg/mL, how many milliliters does the nurse administer to the child?
Express your answer to two significant figures and include the appropriate units.

Answer 39

2.0 mL

Correct answer is shown. Your answer 1.96ml was either rounded differently or used a different number of significant figures than required for this part.

Question 40

In which of the following pairs do both numbers contain the same number of significant figures?

460. 0 L and 4.6×10−4L
461. 0 m and 92.00 m
462. 00064 s and 64000 s
463. 0970 m and 0.907 m

Answer 40

0. 00064 s and 64000 s
1. 0970 m and 0.907 m

All zeros at the end of the decimal numbers 92.0 m and 92.00 m are counted as significant. Because the numbers have differing numbers of zeros, these two measurements do not have the same number of SFs. In 460.0 L and 4.6×10−4L , the second measurement is in scientific notation, so both numbers in the coefficient are counted. The first number is a decimal number with all four numbers counted as significant. Again, the numbers do not have the same number of significant figures.

In 0.0970 m and 0.907 m , both decimal measurements have zeros at the beginning that do not count. The first nonzero digit is used to start counting for each, and they each have 3 SFs. In 0.00064 s and 64000 s , both measurements have 2 SFs because zeros at the beginning of a decimal number and zeros used as placeholders in large non decimal measurements are not significant.

Question 41

The moon is reportedly 2.3890 x 105 miles from Earth. How many significant figures does this number have?

Answer 41

5

Question 42

The number of significant figures in the measurement of 45.030 mm is ________.

Answer 42

five

Question 43

Calculate the total kilocalories if the cup of yogurt contains 12 g of carbohydrate, 9 g of fat, and 9 g of protein.
Express your answer to two significant figures and include the appropriate units.

Answer 43

The energy value for each food type is used to calculate the kilocalories of energy from that food type. The energy values are then added together to give the total energy from cup of yogurt.

Total energy in a cup of yogurt =
(carbohydrate energy) +(fat energy)+(protein energy)=
=(12g×4kcal1g)+(9g×9kcal1g)+(9g×4kcal1g)
=165kcal
=170kcal