UNIT 4: Prealgebra in a Technical World
4.4 Ratios, Rates and Conversions
SWBAT 1. Write ratios to compare quantities.
2. Find unit rates to solve problems.
3. Write conversion facts as conversion ratios.
4. Solve applied problems by converting units (unit analysis).
We live in a world of comparisons. We compare the number of wins to the number of
losses, the number of miles driven to the amount of gas used, the weight of our body fat to our
overall weight, the number of those who voted to those who were eligible to vote, and even
the number of cats to the number of dogs. We write each of these comparisons using ratios.
In this section we study ratios, unit rates, and how to solve and check problems
using conversion fractions.
Ratios
Ratios compare any two quantities.
3
Ratios are written as fractions “ 4 “, using a colon “3:4”, or using the word “to” as in “3 to 4.”
Although all ratios can be written as fractions, fractions are only one kind of a ratio.
Fractions always compare a part to the whole,
𝑝𝑎𝑟𝑡
𝑤ℎ𝑜𝑙𝑒
, while ratios like “cats
to dogs” compare part of a group to another part of a group.
Example 1: More than we care to admit, humans are not always humane when it comes to dogs
and cats. Abandoned animals and their offspring are a big issue in southern Oregon.
a. In Jackson County, the animal shelter took in 2,393 dogs and 3,444 cats in 2008.1 What is
the ratio of dogs to the total number of cats and dogs taken into the shelter?
b. In July 2009, the Rogue Valley Humane Society shelter accepted 95 cats and 22 dogs.2
What is the ratio of dogs to cats accepted in July at this shelter?
1
http://www.co.jackson.or.us/page.asp?navid=1227
335
336
SECTION 4.4: Rates, Ratios and Conversions
Think it Through: a. A total of 2393 dogs needs to be compared to the sum of the cats and
dogs. 𝟐𝟑𝟗𝟑 + 𝟑𝟒𝟒𝟒 = 𝟓𝟖𝟑𝟕, so this ratio is 𝟐𝟑𝟗𝟑 to 𝟓𝟖𝟑𝟕.
b. The total number of dogs is compared only to the total number of cats.
The ratio is 22 dogs to 95 cats.
ANSWER: a. The ratio of dogs to total number of animals taken in was
𝟐𝟑𝟗𝟑
.
𝟓𝟖𝟑𝟕
𝟐𝟐
ANSWER: b. The ratio of dogs to cats accepted at the shelter is 𝟗𝟓 in July, 2009.
Watch the wording when writing and reading ratios. The ratio of cats to
95
22
22
95
dogs, ( ) , is different than that of dogs to cats, ( ).
Sometimes we keep ratios unsimplified; other times, we simplify ratios or even
estimate ratios for easy reading.
Example 2: By the end of the 2011 season, Tom Tebow of the Denver Broncos had completed
167 of 353 attempted passes throughout his career.
a. What is a good estimate for Tom Brady’s pass completion to attempted ratio?
𝟏
𝟏𝟔𝟕
Think it through: The actual ratio is 𝟑𝟓𝟑 ; this is close to and a bit less than .
𝟐
b. What is a good estimate for Tom Brady’s completed to incomplete pass ratio?
Think it through: The actual ratio is
𝟑𝟓𝟑
𝟏𝟔𝟕
𝟐
; this is close to .
𝟏
c. Which of the two ratios above is a fraction, and which is not?
Think it through: The first ratio is a fraction because this is Brady’s ratio of completions to
TOTAL attempted passes. The second ratio is not a fraction because it is
comparing a part to a part of the total passes. In fact, this ratio should be
read “2 to 1” even though it is written as a fraction.
2
Richter, Paula. (2009, August 10). Varner’s the top dog at shelter. Daily Courier, p. 5A.
UNIT 4: Prealgebra in a Technical World
 Check Point 1
As of this writing, digital downloads (DD) sales of music are still less than CD sales. The pie
chart shows the percentage of the market that each media
represents according to an AP report.3
Write and simplify each of these ratios. Tell which of these two
is a fraction.
a. The ratio of digital downloads (DD) to total music sales.
b. The ratio of digital downloads to CD sales.
Unit Rates
When we compare two quantities that have different measures, like miles per hour,
cents per ounce, or dollars per day, we call this ratio a rate.
If vanilla coffee creamer is on sale at $6 for 4 cartons, we have the rate $6
$6
per 4 cartons or 4 . This rate can be simplified and, because we are talking about
money, we will simplify to the cost for one carton. We do this by dividing,
$6
4
=
$1.50
1
, and this gives us the rate $1.50 per carton.
DEFINITION: Unit rates describe how many units of the first type of quantity
correspond to one unit of the second.
While $6/4 is a rate, $1.50 per 1 carton is a special unit rate called a unit price. The first
quantity is dollars, and dollars are being compared to exactly 1 carton. We find unit rates
because they are much easier to use when we compare or calculate. We find unit rates by
dividing.
3
http://www.forbes.com/feeds/ap/2009/08/18/ap6790691.html
337
338
SECTION 4.4: Rates, Ratios and Conversions
Example 3: Levy’s new Scion took 8.2 gal of gas after driving 263.5 miles. How many miles did
the car travel per gallon?
Think it through: Levy estimates by rounding 𝟐𝟒𝟎 ÷ 𝟖 = 𝟑𝟎 mpg and he knows this is a
low estimate. On his calculator, Levy divides 𝟐𝟔𝟑. 𝟓 ÷ 𝟖. 𝟐 = 𝟑𝟐. 𝟏𝟑𝟒𝟏𝟒𝟔.
“About 32 mpg” is close to his estimate, so he accepts his calculator result.
ANSWER: Levy‘s new Scion travelled about 32 miles per 1 gallon of gas.
And because this is per one gallon, this is a unit rate.
Example 4: Dulce downloaded both albums and songs from his favorite music Web site. For 27
tunes he spent $17.73 dollars. What was his average price per tune?
𝟏𝟖
𝟐
Think it through: Dulce estimates first by rounding. His estimate is 𝟏𝟖 ÷ 𝟐𝟕 = 𝟐𝟕 = 𝟑 or
about $0.67 dollars per tune. Dividing exactly on his calculator he finds
𝟏𝟕. 𝟕𝟑 ÷ 𝟐𝟕 = 𝟎. 𝟔𝟓𝟔𝟔𝟔𝟔𝟔𝟔 dollars per tune. This result checks.
ANSWER: Dulce is paying an average of about 66 cents per one tune.
Example 5: Clara is going to hike Mt. McLoughlin in southern Oregon. The trail is 5.5 miles long
and gains 4,395 feet in elevation from bottom to top4. What is the average elevation gain in
feet per mile?
Think it through: Clara rounds to a convenient division fact by rounding both numbers up,
𝟒𝟖𝟎𝟎 ÷ 𝟔 = 𝟖𝟎𝟎 feet per mile. Using a calculator Clara finds 𝟒𝟑𝟗𝟓 ÷
𝟓. 𝟓 = 𝟕𝟗𝟗. 𝟎𝟗𝟎𝟗𝟎𝟗. She decides to use her estimate!
ANSWER: The average elevation gain on the Mt. McLoughlin trail is about 800 ft per
mile.
4
http://www.fs.fed.us/r6/rogue/trails_mcloughlin.html
UNIT 4: Prealgebra in a Technical World
 Check Point 2
a. Melissa drove to Corvallis, Oregon, which was 184 miles from her home. If it took her 3
hours exactly, what was her average miles traveled per hour?
b. It cost Belinda $10.30 for 824 characters of text messaging. How much is she paying per
character?
c. Abdul earns $90 every 8-hour shift. How much does he make per hour?
Once we have unit rates, we solve problems by applying these rates.
Levy’s new Scion averaged 32 mpg.
If Levy plans to visit family in New York
City, how many gallons of gas will he
need to purchase for his trip (see
map5)? How much will this gasoline
cost? Levy has to watch costs carefully;
he is in college right now! In fact, he
plans to bring his food and sleep in the car at campgrounds along his route.
Levy goes to the Web to find the miles he will need to drive. The round trip distance from
Medford, Oregon, to New York, New York, is 5,825 miles. Levy estimates that he will need less
than 200 gallons to travel that distance by quickly rounding and dividing 6000 miles by
30 gallons. When he divides 5,825 by his unit rate of 32 miles per gallon his calculator’s
182 gallons fits with his estimate.
Finally, he researches what gas prices look like across the U.S. this week at the Energy
Information Association (EIA) Web site. Levy finds that the price of gas across the country is
close to, but always below, $4 per gallon. He uses the $4 per gallon figure and decides that the
gasoline for his trip will cost no more than $728. He is going to budget $750 for gas and
another $100 for an oil change and miscellaneous car expenses.
5
MapQuest: http://www.mapquest.com/directions
339
340
SECTION 4.4: Rates, Ratios and Conversions
Levy had taken chemistry, and to check that he is multiplying and dividing his figures
correctly he uses a unit analysis:
5825 𝑚𝑖𝑙𝑒𝑠 1 𝑔𝑎𝑙𝑙𝑜𝑛 4 𝑑𝑜𝑙𝑙𝑎𝑟𝑠
5825 ∗ 4
𝑑𝑜𝑙𝑙𝑎𝑟𝑠
∙
∙
=
≈ 729
1 𝑡𝑟𝑖𝑝
32 𝑚𝑖𝑙𝑒𝑠 1 𝑔𝑎𝑙𝑙𝑜𝑛
32
𝑡𝑟𝑖𝑝
Levy’s check method, unit analysis, is used in technical, business, medical and scientific
fields to set up computation so that the correct operations are used in calculating.
Unit Analysis
DEFINITION: Unit analysis is the method of solving problems by multiplying
ratios with their units included, as shown in Levy's work in the last problem. The
units of the required result are all that are left after units which occur in both a
numerator and a denominator are eliminated.
By writing the units with the quantities in each ratio, we can quickly determine whether
the units we are working with will solve our initial problem. We set up problems by knowing the
units of our answer first. Then we think through which units we wish to eliminate and which
we want to keep.
Often the ratios we write are made from conversion facts. For instance, we know that
there are 24 hours in one day so this is a conversion fact.
DEFINITION: Conversion ratios are equal to one and are written using conversion
facts. The fact that 24 hours is one day gives us two conversion ratios:
24 ℎ𝑜𝑢𝑟𝑠
1 𝑑𝑎𝑦
and
1 𝑑𝑎𝑦
24 ℎ𝑜𝑢𝑟𝑠
.
We know many conversion facts because we use them so often. For example, we know
that sixty minutes is one hour, 60 min = 1 hour. We can find the conversion facts that we do
not know online, in dictionaries and often in our textbooks. Table 4.1 gives several conversion
facts that we will use in this course.
UNIT 4: Prealgebra in a Technical World
TABLE 4.1
Length
Weight
Volume
Time
1 mile
5280 ft
1 lb
16 oz
1 oz
29.6 mL
1 year
365.25 days
1 in
2.54 cm
1 ton
2,000 lbs
1 cup
8 oz
1 min
60 sec
1 mile
1.61 km
1 kg
2.2 lbs
1.06 qt
1L
1 hour
60 min
We use the facts in this table to study the method of unit analysis.
RULE: To use unit analysis, follow these steps.
1. Determine the units of the quantities to start with and the units for the
answer.
2. Starting with the original number and its unit(s), then write conversion ratios
to eliminate unnecessary units until the unit(s) of the answer is reached.
3. Multiply the quantities in the numerators and divide by quantities in the
denominators.
4. Simplify, if necessary, and keep the units of your final answer.
(Remember to estimate along the way to check your work.)
Example 6: During August, 2009, while this book was being written, Andrew Howland Moyer,
whose mother was a RCC student, was born at Three Rivers Hospital in Grants Pass. Andrew
weighed in at 4.19 kg. What did Andrew weigh in pounds? What did Andrew weigh in pounds
and ounces?
Think it through: Convert kilograms to pounds and convert decimal pounds to ounces.
4.19 kg
=______lbs.
We start with kg and want to end
with lbs.
4.19 kg ∙ 1 𝑘𝑔 =_____ lbs.
Write the conversion fact needed.
(The kg unit is then eliminated.)
4.5 ∙ 2 ≈ 9
Estimate the weight at about 9 lbs.
2.2 𝑙𝑏𝑠
341
342
SECTION 4.4: Rates, Ratios and Conversions
2.2 𝑙𝑏𝑠
4.19 kg ∙ 1 𝑘𝑔 = 9.218 lbs.
0.218 lbs ∙
16 𝑜𝑧
1 𝑙𝑏
Use a calculator to multiply.
= 3.488≈ 3.5 oz.
Convert the decimal fraction of a
pound to ounces.
𝟏
ANSWER: Andrew weighs about 9 lbs. 3𝟐 oz. and Mom, Dad, Brother, Sister, and
Andrew are all doing well.

Check Point 3
Amanda has an 8 cup Thermos. Amanda knows that four cups equal one quart. Will her
two liter soda fit in this container? Write a unit analysis to justify your answer.
Unit analysis works even when we do not understand the size of the measurements we
use.
Roman Volume6
Example 7: The volume measures used in Ancient Rome included
those in the table at right. Using this table, how many gemin are
1 kognee = 12 gemin
needed to make one kulee?
1 amphora = 8 kognee
Think it through: We do not know these units! Use unit analysis to
analyze the problem and justify our answer.
1 kulee = 20 amphora
1 𝑘𝑢𝑙𝑒𝑒 (
___𝑎𝑚𝑝ℎ𝑜𝑟𝑎
___ 𝑘𝑜𝑔𝑛𝑒𝑒
____𝑔𝑒𝑚𝑖𝑛
)(
)(
)
___ 𝑘𝑢𝑙𝑒𝑒
___ 𝑎𝑚𝑝ℎ𝑜𝑟𝑎 ___ 𝑘𝑜𝑔𝑛𝑒𝑒
Write the unit
analysis.
20 𝑎𝑚𝑝ℎ𝑜𝑟𝑎
8 𝑘𝑜𝑔𝑛𝑒𝑒
12 𝑔𝑒𝑚𝑖𝑛
)(
)(
)
1 𝑘𝑢𝑙𝑒𝑒
1 𝑎𝑚𝑝ℎ𝑜𝑟𝑎 1 𝑘𝑜𝑔𝑛𝑒𝑒
Fill in the
conversion fact
numbers.
1 𝑘𝑢𝑙𝑒𝑒 (
(Remember: units
divide away!)
1 ∙ 20 ∙ 10 ∙ 10 ≈ 2,000
1 ∙ 20 ∙ 8 ∙ 12 = 160 ∙ 12 = 1,920 𝑔𝑒𝑚𝑖𝑛
6
http://www.convert-me.com/en/ accessed 6/29/10
Estimate
Multiply numbers
in the numerator.
UNIT 4: Prealgebra in a Technical World
ANSWER: One kulee equals 1,920 gemin.
 Check Point 4
Not only do we have inches, feet, and yards, in our U.S. system of
measure, but surveyors also measure lengths in links, rods, and chains.
These are related using the table at right. Using this table, how many
links are there in a mile?
U.S. Survey Measure
1 rod = 25 links
1 chain = 4 rods
1 mile = 80 chains
As in many other states, Oregon law requires that packages be labeled with their full
price and their unit price.7
Unfortunately, one company may label its product using the metric system while
another company labels its product in U.S. units. Even if both use the U.S. system, one could
measure in quarts while the other uses liquid ounces.
Using unit analysis and our conversion facts, we can often find the best buy using
mental math.
Example 8: Mariah is shopping for split pea soup. She finds her two favorite brands. The Green
Brand is $2.19 for 12 ounces with a listed unit price of about $0.18 per ounce. The Yellow
Brand is $2.59 for 500 mL with a listed unit price of $0.005 per mL . Mariah wants to know
which brand is the best buy.
Think it through: This is a job for unit analysis. Mariah, a nursing student, knows how to do
this in her head. Mariah knows that 1 ounce is about 30 mL
(
$0.18
1 ounce Mariah decides to convert the
)
) ∙(
1 ounce
30 𝑚𝐿
Green soup to a unit price per mL.
$0.18
1 ounce
$0.18
(1 ounce) ∙ ( 30 𝑚𝐿 ) = 30 𝑚𝐿 Mariah accepts her unit analysis.
$0.18 3 $0.06
Mariah simplifies the ratio.
÷ =
30 𝑚𝐿 3 10 𝑚𝐿
7
http://oregon.gov/ODA/MSD/labels.shtml
343
344
SECTION 4.4: Rates, Ratios and Conversions
Dividing by 10 changes the place
$0.06
= $0.006 per 𝑚L value from hundredths to
10 𝑚𝐿
thousandths.
ANSWER: Mariah knows now that Yellow Brand is the best buy.
 Check Point 5
Which is the best buy? A bar of soap that is 250 grams for $2.99 or 4 ounces of soap for $1.99?
Use unit analysis to analyze and justify your result.
Perhaps you have been able to solve many of the problems in this section without using
unit analysis. Good job! This shows that you are thinking. Still, you will want to practice unit
analysis. Technical problems and problems that involve our money often contain many
conversions, including changing both the numerator and denominator to different units. Unit
analysis tells us that we have thought through these problems correctly.
The next problems may require that we change units in both the numerator and
denominator.
Example 9: Tyrone is filling in his financial aid paperwork. He has recently taken a job that pays
Oregon’s minimum wage of $8.80 per hour. He is asked to estimate his gross pay for the
coming year, but Tyrone has not even received a paycheck yet!
Think it through: Tyrone uses unit analysis beginning with his hourly pay at the start and
ending with his annual gross pay. Then he fills in the conversion ratios.
Tyrone is working 5 days each week for 8 hours a day, and he gets two
weeks off with no pay.
Tyrone estimates ($8)(40 hours per week)(50 weeks per year) is
$320 ∙ 50 is $16,000. He writes a unit analysis:
8.80 𝑑𝑜𝑙𝑙𝑎𝑟𝑠
8 ℎ𝑜𝑢𝑟𝑠
5 𝑤𝑜𝑟𝑘 𝑑𝑎𝑦𝑠 50 𝑤𝑜𝑟𝑘 𝑤𝑒𝑒𝑘𝑠
∙
∙
∙
1 ℎ𝑜𝑢𝑟
1 𝑤𝑜𝑟𝑘 𝑑𝑎𝑦 1 𝑤𝑜𝑟𝑘 𝑤𝑒𝑒𝑘 1 𝑤𝑜𝑟𝑘 𝑦𝑒𝑎𝑟
UNIT 4: Prealgebra in a Technical World
Tyrone divides away units to make sure he has set things up correctly:
Then he multiplies and finds:
8.80 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 8 5
50
17,600 𝑑𝑜𝑙𝑙𝑎𝑟𝑠
∙ ∙ ∙
=
1
1 1 1 𝑤𝑜𝑟𝑘 𝑦𝑒𝑎𝑟
1 𝑦𝑒𝑎𝑟
ANSWER: Tyrone enters $17,600 on his financial aid form for his gross annual
expected wages.
Example 10: The Earth rotates about its axis. At the 42nd parallel, the border between Oregon
and California, the distance around the Earth is about 18,490 miles. How much of this distance
will you travel during a 50-minute math class?
Think it through: Estimate
18490 𝑚𝑖𝑙𝑒𝑠
1 𝑑𝑎𝑦
18490 𝑚𝑖𝑙𝑒𝑠
(
1 𝑑𝑎𝑦
1 𝑑𝑎𝑦
18490 𝑚𝑖𝑙𝑒𝑠
(
1
24
=
=
??
3,000
18,000
24
4
1 ℎ𝑜𝑢𝑟
1
4
≈ 700 miles in a little less than 1 hour.
We start with miles per day and
end with miles per math class.
50 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
1 𝑐𝑙𝑎𝑠𝑠
50 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
) ∙ (24 ℎ𝑜𝑢𝑟𝑠) ∙ (60 𝑚𝑖𝑛𝑢𝑡𝑒𝑠)∙(
1
3,000
1 𝑚𝑎𝑡ℎ 𝑐𝑙𝑎𝑠𝑠
1 ℎ𝑜𝑢𝑟
1 𝑑𝑎𝑦
=
𝑚𝑖𝑙𝑒𝑠
) ∙ (24 ℎ𝑜𝑢𝑟𝑠) ∙ (60 𝑚𝑖𝑛𝑢𝑡𝑒𝑠)∙ (
18490 𝑚𝑖𝑙𝑒𝑠
(
1 𝑑𝑎𝑦
18,000
1 𝑐𝑙𝑎𝑠𝑠
)=
Write the conversion facts.
)=
Eliminate the units.
50
) ∙ (24 ) ∙ (60 )∙(1 𝑐𝑙𝑎𝑠𝑠) = 642.013888889 Use the calculator and multiply
numerators and divide by each
denominator.
ANSWER: During one 50 minute class, people near the 42nd parallel travel about
642 miles around the axis of the Earth.
 Check Point 6
If you are offered a job that pays $40,000 per year and requires you to work 283 days per year,
how much do you make per hour if a work day is 8 hours?
345
346
SECTION 4.4: Rates, Ratios and Conversions
UNIT 4: Prealgebra in a Technical World
4.4 Exercise Set
347
Name _______________________________
Skills
Convert these lengths by multiplying by their conversion ratios. Round to the hundredths.
1. 16.17 m =
yd 2. 90.75 yd =
m
3. 5.012 km =
mi 4.
7.25 mi =
km
5. 9.24 cm =
ft 6.
58.75 ft =
cm
7. 861.2 mm =
in 8.
71.875 in =
mm
Convert these capacities by multiplying by their conversion ratios. Round to 2 decimal places.
9.
2.7 L =
qt 10. 17 qt =
11. 2.4 kL =
gal 12. 18.5 gal =
13. 3.4 L =
cup 14. 4 cups =
15. 32.1 mL =
oz 16. 6.25 oz =
L
kL
L
mL
Convert these masses and weights using conversion ratios. Round to 2 decimal places.
17. 42.9 g =
oz 18. 1.5 oz =
g
19. 1.3 kg =
lbs 20. 161.5 lbs =
kg
21. 226 kg =
lbs 22. 4.75 lbs =
kg
23. 200 mg =
oz 24. 6.5 oz =
mg
Convert the units by multiplying by their conversion ratio.
25. 0.5 mi =
ft 26. 184 oz =
lbs
27. 333 in =
ft 28. 208 ft =
yd
29. 44 gal =
qt 30. 7,500 lbs =
tons
31. 45 cups =
oz 32. 36 oz =
cups
Applications
UPS
33.
Which is more, a two-liter bottle of soda or a two-quart bottle of soda? Explain.
34.
Anna, from Spain, is shopping in America. She bought a fifty-one fluid ounce bottle of
olive oil to make her famous paella. She doesn't understand ounces; how many liters are
in the bottle?
348
SECTION 4.4: Rates, Ratios and Conversions
35.
A recipe calls for 240 mL of peanut butter. How many cups of peanut butter will that be?
36.
Louise is comparing a 1.36 kg jar of peanut butter she bought in Canada while camping to
what she has at home. About how many pounds would that be?
37.
Tony got a birth announcement from his brother in Italy. He is the proud uncle of a new
baby girl who weights 3.5 kg. How many pounds and ounces is that?
38.
Convert these measures so you can send this recipe to your European friend.
a. 2.5 cups of flour is _____________________________mL.
b. 0.5 tsp. of salt is _______________________________mL.
c. I tsp. each of baking soda and vanilla is____________ mL. each
d. 1 cup each of white sugar and brown sugar is ____________ mL. each
e. 2 eggs are ____________________________________eggs
f. 2 cups of chocolate chips are _____________________mL.
g. Bake at 375℉ is _______________________________℃.
39. Oregon is 98,386 square miles, including 2,383 square miles of inland water. Portland
State University’s estimate is 3,871,859 for Oregon's 2011 population.
a. On average, how many square miles are there per person in Oregon in 2011? (Round
to the thousandth of a square mile.)
b. How many square feet per person were there in Oregon in 2009?
40. A Canadian athlete ran a 100-m race in 19.83 seconds. An American athlete ran a
100-yard race in the same time. Who ran faster?
41. A road sign in Canada says the speed limit is 90 km/hr. What is the speed in mph?
42. If the U.S. changed to the metric system, a "quarter-pounder" might be called a
_______________ "kilogrammer?" (Round to the nearest thousandth of a kg.)
UNIT 4: Prealgebra in a Technical World
43.
You are shopping in Mexico and find some fabric that you want. Your pattern calls for 3.5
yards, and the fabric sells for 25.98 MXN (“Mexican dollars” = pesos) per meter.
a. About how many meters do you need to buy?
b. About how much will the fabric cost?
c. What is the USD (US dollar) equivalent for your answer in part b if 1 USD = 12.72 MXN?
44. It's been determined that the Himalayan Mountains are growing higher at a rate of about
2.4 inches per year. If the mountains continue growing at that rate, by how many feet will
the elevation increase in the next 100 years?
45. Imagine that water is leaking from a container at a rate of 0.5 mL /minute. If this rate
does not change, how many liters of water will be lost in a week?
46. A student earns $9.50 per hour and works 30 hours per week. She has two weeks of
unpaid vacation. How much will she earn in a year?
47. What are the dimensions of an 8.5 inch x 11 inch sheet of paper in centimeters?
48. A football field has a 900-foot perimeter. How many times would a person need to walk
around the field to have walked 4 miles?
49. How long in miles are one trillion one dollar bills laid end to end? (A dollar bill is 6 inches
long.)
50. Jeremy went sailing with a friend. They sailed 25 nautical miles. How many miles did they
travel, if one nautical mile = 1.852 km?
349
350
SECTION 4.4: Rates, Ratios and Conversions
Review and Extend
The following problems will be easier if you use scientific notation with unit analysis.
51. One thousand seconds is about _____________________minutes.
52. One million seconds is about _______________________days.
53. One billion seconds is about ________________________years.
54. One trillion seconds is about ________________________years.
55. The Earth travels an average of 583,707,915 miles around the sun each year. How fast is
the Earth traveling in miles per hour?
56. The speed of light is 983,571,056.43045 ft/sec and is the speed limit of the universe. How
fast is that in miles per hour?
57. Recall problem 60 in Exercise 3.6. If this tire were rolling down the road, how many
rotations would it make in a mile?
58. Going retro, you decide to carpet your house with carpet tiles. Each “groovy” tile is
0.16 m2, and each box has twelve tiles. You must buy whole boxes.
a. How many square feet will a box cover?
b. If your room is 16 feet by 18 feet, how many boxes will you need to buy to cover the
floor?