## Engage NY Eureka Math 8th Grade Module 2 Lesson 8 Answer Key

### Eureka Math Grade 8 Module 2 Lesson 8 Exercise Answer Key

Exercise 1.

The Federal Reserve states that the average household in January of 2013 had $7,122 in credit card debt. About how many times greater is the U.S. national debt, which is $16,755,133,009,522? Rewrite each number to the nearest power of 10 that exceeds it, and then compare.

Answer:

Household debt=7122<9999<10000=10^{4}.

U.S.debt=16 755 133 009 522<99 999 999 999 999<100 000 000 000 000=10^{14}.

\(\frac{10^{14}}{10^{4}}\) =10^{14-4}=10^{10}. The U.S. national debt is 10^{10} times greater than the average household’s credit card debt.

Exercise 2.

There are about 3,000,000 students attending school, kindergarten through Grade 12, in New York. Express the number of students as a single-digit integer times a power of 10.

Answer:

3 000 000=3×10^{6}

The average number of students attending a middle school in New York is 8×10^{2}. How many times greater is the overall number of K–12 students compared to the average number of middle school students?

Answer:

\(\frac{3 \times 10^{6}}{8 \times 10^{2}}\)=\(\frac{3}{8}\)×\(\frac{10^{6}}{10^{2}}\)

= \(\frac{3}{8}\)×10^{4}

= 0.375×10^{4}

There are about 3,750 times more students in K–12 compared to the number of students in middle school.

Exercise 3.

A conservative estimate of the number of stars in the universe is 6×10^{22}. The average human can see about 3,000 stars at night with his naked eye. About how many times more stars are there in the universe compared to the stars a human can actually see?

Answer:

\(\frac{6 \times 10^{22}}{3 \times 10^{3}}\))=\(\frac{6}{3}\)×\(\frac{10^{22}}{10^{3}}\) =2×10^{22-3}=2×10^{19}

There are about 2×10^{19} times more stars in the universe compared to the number we can actually see.

Exercise 4.

The estimated world population in 2011 was 7×10^{9}. Of the total population, 682 million of those people were left-handed. Approximately what percentage of the world population is left-handed according to the 2011 estimation?

Answer:

682 000 000≈700 000 000=7×10^{8}

\(\frac{7 \times 10^{8}}{7 \times 10^{9}}\)=\(\frac{7}{7}\)×\(\frac{10^{8}}{10^{9}}\)

=1×\(\frac{1}{10}\)

=\(\frac{1}{10}\)

About one-tenth of the population is left-handed, which is equal to 10%.

Exercise 5.

The average person takes about 30,000 breaths per day. Express this number as a single-digit integer times a power of 10.

Answer:

30000=3×10^{4}

If the average American lives about 80 years (or about 30,000 days), how many total breaths will a person take in her lifetime?

Answer:

(3×10^{4} )×(3×10^{4} )=9×10^{8}

The average American takes about 900,000,000 breaths in a lifetime.

### Eureka Math Grade 8 Module 2 Lesson 8 Problem Set Answer Key

Students practice estimating size of quantities and performing operations on numbers written in the form of a single-digit integer times a power of 10.

Question 1.

The Atlantic Ocean region contains approximately 2×10^{12} gallons of water. Lake Ontario has approximately 8,000,000,000,000 gallons of water. How many Lake Ontarios would it take to fill the Atlantic Ocean region in terms of gallons of water?

Answer:

8 000 000 000 000=8×10^{12}

\(\frac{2 \times 10^{16}}{8 \times 10^{12}}\)=\(\frac{2}{8}\)×\(\frac{10^{16}}{10^{12}}\)

=\(\frac{1}{4}\)×10^{4}

=0.25×10^{4}

=2500

2,500 Lake Ontario’s would be needed to fill the Atlantic Ocean region.

Question 2.

U.S. national forests cover approximately 300,000 square miles. Conservationists want the total square footage of forests to be 300,000^{2} square miles. When Ivanna used her phone to do the calculation, her screen showed the following:

a. What does the answer on her screen mean? Explain how you know.

Answer:

The answer means 9×10^{10}. This is because:

(300 000)^{2}=(3×10^{5})^{2}

=3^{2}×(10^{5})^{2}

=9×10^{10}

b. Given that the U.S. has approximately 4 million square miles of land, is this a reasonable goal for conservationists? Explain.

Answer:

4 000 000=4×10^{6}. It is unreasonable for conservationists to think the current square mileage of forests could increase that much because that number is greater than the number that represents the total number of square miles in the U.S,

9×10^{10}>4×10^{6}.

Question 3.

The average American is responsible for about 20,000 kilograms of carbon emission pollution each year. Express this number as a single-digit integer times a power of 10.

Answer:

20 000=2×10^{4}

Question 4.

The United Kingdom is responsible for about 1×10^{4} kilograms of carbon emission pollution each year. Which country is responsible for greater carbon emission pollution each year? By how much?

2×10^{4}>1×10^{4}

Answer:

America is responsible for greater carbon emission pollution each year. America produces twice the amount of the U.K. pollution.

### Eureka Math Grade 8 Module 2 Lesson 8 Exit Ticket Answer Key

Most English-speaking countries use the short-scale naming system, in which a trillion is expressed as 1,000,000,000,000. Some other countries use the long-scale naming system, in which a trillion is expressed as 1,000,000,000,000,000,000,000. Express each number as a single-digit integer times a power of ten. How many times greater is the long-scale naming system than the short-scale?

Answer:

1 000 000 000 000=10^{12}

1 000 000 000 000 000 000 000=10^{21}

\(\frac{10^{21}}{10^{12}}\). The long-scale is about 10^{9} times greater than the short-scale.