Math 120- Quantitative Literacy: 3B Homework

Briefly describe scientific notation. How is it useful for writing large and small numbers?

Scientific notation is a format in which a number is expressed as a number between 1 and 10 multiplied by a power of 10. It is useful for writing large and small numbers because it offers a way to save space and avoid errors in calculations. 

How is scientific notation useful for making approximations?

Scientific notation is useful in making approximations because it provides a quick and easy way to decide if calculated values are reasonable. 

Describe the three common ways of expressing the scale of a map or model.

A scale can be described verbally, in words such as “One centimeter represents one kilometer,” graphically, such as a marked mini ruler of a map, or as a ratio, where one unit is described in terms of the other.

How would you show a scale of 1 cm = 100 km graphically? 

A mini ruler 1 cm long marked “100 km” 

How would you describe 1 cm = 100 km as a ratio?

1/10,000,000

The earth is about 12,760 km in diameter and about 150 million kilometers away from the sun. The nearest starts besides the Sun are about 4.3 light-years away (1 light year = 9.5 ×10¹² km). At a scale of 1 to 10 billion, the Sun would be about the size of a grapefruit. How big and how far away would the Earth be on this scale? How far would the nearest stars (besides the Sun) be?

A.) Approximately how big would the Earth’s diameter be on this scale?
B.) Approximately how far away would the two objects be on this scale?
C.) Approximately how far would the nearest stars (beside the Sun) be on this scale?

A.) 1.3 mm
B.) 15 m
C.) 4100 km

Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. 

I read a book that had 10⁵ words in it.

The statement makes sense because it is possible for a book to contain 100,000 words.

Rewrite the following statement using a number in scientific notation.

My new music player has a capacity of 320 gigabytes. (Recall that giga means billion.)

My new music player has a capacity of ______ bytes.

3.2 × 10¹¹

What is the order of magnitude estimate for the number of steps you take in an average day?

A.) The oder of magnitude estimate is 375 to 500 steps; assuming an average person walks ¼ of a mile per day.
B.) The order of magnitude is 100 to 200 steps; assuming an average person walks 8 miles per day.
C.) The order of magnitude estimate is 375 to 575 steps; assuming an average person walks 16 miles per day.
D.) The order of magnitude estimate is 3000 to 4000 steps; assuming an average person walks 2 miles per day.

D.) The order of magnitude estimate is 3000 to 4000 steps; assuming an average person walks 2 miles per day.

Make an order of magnitude estimate of the following quantity. Explain the assumption used in your estimation. 

The number of miles the average person travels in a car in a year (as either driver or passenger)

A.) 3600 miles; assuming the average person travels 10 miles per day
B.) 360 miles; assuming the average person travels 1 mile per day
C.) 36,000 miles; assuming the average person travels 100 miles per day 
D.) 72,000 miles, assuming the average person travels 200 miles per day

A.) 3600 miles; assuming the average person travels 10 miles per day

Use the data in the table below to determine how many average candy bars an adult would have to eat to supply the energy needed for six hours of running.

Item:
Energy released by metabolism of 1 average candy bar. 1 × 10⁶
Energy needed for 1 hour of running (adult). 3.9 × 10⁶

The average adult would have to eat _____ average candy bars.

23

There are approximately 2.5 million deaths per year in county A. Express this quantity as deaths per minute.

In country A, there are _____ deaths/min.

4.8

An issue of a magazine contained the following statement. 

Dropping less than two inches per mile after emerging from the mountains, a river drains into the ocean. One day’s discharge at its mouth, 3 trillion gallons, could supply all of country A’s households for six months. 

Based on this statement, determine how much water an average household uses each month. Assume that there are 100 million households in country A.

Country A uses approximately ______ gallons per household per month.

5000

Convert the following number from scientific notation to ordinary notation.

3 × 10^-4

0.0003

Convert to scientific notation.

18000

1.8 × 10⁴

Perform the indicated computation. Write the answer in scientific notation. 

(4 × 10⁵) (2 × 10³)

8 × 10⁸

A county’s people consume 6.1 billion pounds of candy (excluding chewing gum) per year. Express this quantity in terms of pounds per person per month. Note that the population of the country is 305 million.

The amount of candy consumed is approximately _____ pounds per person per month.

1.7

order of magnitude

specifies a broad range of values, usually within one or two powers of ten, such as “in the ten thousands” or “in the millions”