Use and Abuse of Percentages
Putting Numbers in Perspective
Dealing with Uncertainty
Index Numbers
most missed questions for quiz 3A/3B
100
There are 171 potentially active volcanoes in the United States and its territories. There are about 1351 potentially active volcanoes worldwide.
What percent of the total number of potentially active volcanoes are located in the United States and its territories?
12.7%
100
Write the number in scientific notation.
0.00000353
3.53 × 10^-6
100
State the number of significant digits and the implied precision of the given number.
3.62253 mi
6 significant digits
The number is precise to the nearest hundred-thousandth of a mile
100
What is the Consumer Price Index (CPI)? How is it supposed to be related to inflation?
Choose the correct answer below.
A. It is a way of comparing the prices consumers pay for products to the prices producers (manufacturers) pay for the goods they purchase. It allows one to see how prices have changed with time, and therefore measures inflation.
B. It is a way of measuring the prices consumers pay for products. It allows one to see how prices have changed with time, and therefore measures inflation.
C. It is a way of measuring consumer attitudes. It can gauge whether people are likely to be spending or saving, which, in turn, is related to inflation.
B
100
Rewrite the following statement using scientific notation.
My hard drive has a capacity of 3.1 terabytes. (Recall that tera means "trillion.")
3.1 xx 10^12
200
An antique store collects 2% sales tax on all sales. If the total sales (before tax) were $1,547.63, how much money should be collected in sales tax?
*round your answer to the nearest cent, if needed
$30.95
200
Use scientific notation to perform the following operations. Leave your answer in scientific notation.
(3 xx10^2 ) ( 4xx10^3 )
1.2 × 10^6
200
Under the standard rules for counting significant digits, which of the following numbers has the most significant digits, and how many?
1.04 1.040 0.000040
1.040 has 4 significant digits
200
Look at the gasoline price index in the table. What does the 2015 price index of 109.1 mean? Explain your reasoning.
A.Gas in 2015 cost 1.091 times as much as gas in 2005, because the ratio of the gas price index in 2015 to the gas price index in 2005 is 1.091.
B.Gas in 2015 cost 1.091cents per gallon, because the gas price index measures the cost per gallon.
C.Gas in 2015 cost 109.1cents per gallon, because the gas price index measures the cost per gallon.
D.Gas in 2015 cost 109.1 times as much as gas in 2005, because the ratio of the gas price index in 2015 to the gas price index in 2005 is 109.1.
A
200
As of 2022, the life expectancy (at birth) of women in a particular country (79.9 years) is _____ percent greater than the life expectancy of men in that same country (77.4 years).
*round to the nearest tenth percent
3.2%
300
True or False: EXPLAIN your reasoning.
50% of the hotels have a restaurant, and 40% have a swimming pool, so 90% of hotels in town have a restaurant or a pool.
False: Some hotels with a restaurant may also have a pool
300
Write the number in scientific notation.
A company produces 173,000 small appliances in one year.
1.73 × 10^5
300
Find the absolute and relative errors in the following situation.
The true price of a gift you purchased by mail order is $18.48, but you are billed $19.32.
Absolute error: $0.84
Relative error: 4.5%
300
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.
The prices of cars have risen steadily, but when the prices are adjusted for inflation, cars are cheaper today than they were a couple of decades ago.
A.The statement does not make sense. The price of cars is based on the inflation rate. So, the cost of cars today should be higher than a couple of decades ago.
B.The statement does not make sense. The price of cars is based on the inflation rate. So, the cost of cars today should be the same as a couple of decades ago.
C.The statement does not make sense. Since the price of cars has increased, they cannot be cheaper today than they were a couple of decades ago.
D.The statement makes sense. The rate at which car prices increased could be lesser than the inflation rate, meaning cars are relatively cheaper today than a couple of decades ago.
D
300
Simon's monthly take-home pay (after taxes) is
$2300. If he pays 22 % of his gross pay (before taxes) in tax, what is his gross pay?
*round to the nearest cent
$2948.72
400
The (after-tax) cost of a laptop is $860. The local tax rate is 7.4%. What is the retail (pre-tax) price?
*round your answer to the nearest cent as needed
$800.74
400
If a recipe calls for 1.5 cups of flour to make 8 pancakes, how much flour do you need to make 24 pancakes?
4.5 cups of flour
400
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.
Based on the projection from the U.S. Congressional Budget Office, we can be very confident that next year's federal deficit will be $943.45 billion.
This statement does not make sense because there are too many significant digits.
400
Suppose the current cost of gasoline is $3.30 per gallon. Find the current price index using the 1975 price as the reference value. In 1975, the cost of gasoline was 56.7 cents per gallon. Round to the nearest tenth as needed.
**note that 1975 is in CENTS**
582.0
400
The total (after-tax) cost of a laptop computer is $837. The local sales tax rate is 5.5%. What is the retail (pre-tax) price?
*round to the nearest cent
$793.36
500
The population of Placerville grew from 4960 a decade ago to 6620 today. What are the Absolute Change and the Relative Change?
*round answers to the nearest tenth, if necessary
abs change= 1660 people
rel change- 33.5%
500
If half an inch on a blueprint represents 3 feet in reality, find the actual dimensions of a kitchen with a length of 3 inches and a width of 1.5 inches on the blueprint.
Length = 18 ft
Width= 9 ft
500
In 2015 and 2016, a mosquito-borne disease called Zika fever spread through much of the Americas and a few other areas of the world. Researchers studying the progression of the Zika epidemic faced at least two major challenges in determining how many people had been infected: (1) many cases of Zika infection occurred in poor or remote areas where medical diagnosis was not available, and (2) some people who were suffering from Zika infection were misdiagnosed as having other diseases, and vice versa.
Problem (1) is a ____________error.
Problem (2) is a ____________error.
1. systematic
2. random
500
Suppose it cost $ 13.41 to fill a gas tank in 2000. How much would it have cost to fill the same tank in 1975? Round to the nearest hundredth as needed. Use the table below.
$4.91
500
If the sales in your pizza restaurant increase by
8% one year and decrease by 4% the following year, your sales are up by_____% over two years
3.68%