## Engage NY Eureka Math 8th Grade Module 1 Lesson 7 Answer Key

### Eureka Math Grade 8 Module 1 Lesson 7 Exercise Answer Key

Exercise 1.

Let M=993,456,789,098,765. Find the smallest power of 10 that will exceed M.

Answer:

M=993 456 789 098 765 < 999 999 999 999 999 < 1 000 000 000 000 000=10^{15}. Because M has 15 digits, 10^{15} will exceed it.

Exercise 2.

Let M=78,491\(\frac{899}{987}\). Find the smallest power of 10 that will exceed M.

Answer:

M=78491\(\frac{899}{987}\) < 78492<99999<100 000=10^{5}.

Therefore, 10^{5} will exceed M.

Exercise 3.

Let M be a positive integer. Explain how to find the smallest power of 10 that exceeds it.

Answer:

If M is a positive integer, then the power of 10 that exceeds it will be equal to the number of digits in M. For example, if M were a 10-digit number, then 10^{10} would exceed M. If M is a positive number, but not an integer, then the power of 10 that would exceed it would be the same power of 10 that would exceed the integer to the right of M on a number line. For example, if M=5678.9, the integer to the right of M is 5,679. Then based on the first explanation, 10^{4} exceeds both this integer and M; this is because M=5678.9<5679<10 000=10^{4}.

Exercise 4.

The chance of you having the same DNA as another person (other than an identical twin) is approximately 1 in 10 trillion (one trillion is a 1 followed by 12 zeros). Given the fraction, express this very small number using a negative power of 10.

\(\frac{1}{10000000000000}\)

Answer:

\(\frac{1}{10000000000000}\) = \(\frac{1}{10^{13}}\)

= 10^{-13}

Exercise 5.

The chance of winning a big lottery prize is about 10^{-8}, and the chance of being struck by lightning in the U.S. in any given year is about 0.000 001. Which do you have a greater chance of experiencing? Explain.

Answer:

0.000 001=10^{-6}

There is a greater chance of experiencing a lightning strike. On a number line, 10^{-8} is to the left of 10^{-6}. Both numbers are less than one (one signifies 100% probability of occurring). Therefore, the probability of the event that is greater is 10^{-6}—that is, getting struck by lightning.

Exercise 6.

There are about 100 million smartphones in the U.S. Your teacher has one smartphone. What share of U.S. smartphones does your teacher have? Express your answer using a negative power of 10.

Answer:

\(\frac{1}{100000000}\)=\(\frac{1}{10^{8}}\)=10^{-8}

### Eureka Math Grade 8 Module 1 Lesson 7 Problem Set Answer Key

Question 1.

What is the smallest power of 10 that would exceed 987,654,321,098,765,432?

Answer:

987 654 321 098 765 432<999 999 999 999 999 999<1 000 000 000 000 000 000=10^{18}

Question 2.

What is the smallest power of 10 that would exceed 999,999,999,991?

Answer:

999 999 999 991<999 999 999 999<1 000 000 000 000=10^{12}

Question 3.

Which number is equivalent to 0.000 000 1: 10^{7}or 10^{-7}? How do you know?

Answer:

0.000 000 1=10^{-7}. Negative powers of 10 denote numbers greater than zero but less than 1. Also, the decimal 0.000 000 1 is equal to the fraction \(\frac{1}{10^{7}}\) which is equivalent to 10^{-7}.

Question 4.

Sarah said that 0.000 01 is bigger than 0.001 because the first number has more digits to the right of the decimal point. Is Sarah correct? Explain your thinking using negative powers of 10 and the number line.

Answer:

0.000 01= \(\frac{1}{100000}\) = 10^{-5} and 0.001= \(\frac{1}{1000}\) =10^{-3}. On a number line, 10^{-5} is closer to zero than 10^{-3}; therefore, 10^{-5} is the __smaller__ number, and Sarah is incorrect.

Question 5.

Order the following numbers from least to greatest:

Answer:

10^{-99}<10^{-17}<10^{-5}<10^{5}<10^{-14}<10^{30}

### Eureka Math Grade 8 Module 1 Lesson 7 Exit Ticket Answer Key

Question 1.

Let M=118,526.65902. Find the smallest power of 10 that will exceed M.

Answer:

Since M=118,526.65902<118,527<1,000,000<10^{6}, then 10^{6}will exceed M.

Question 2.

Scott said that 0.09 was a bigger number than 0.1. Use powers of 10 to show that he is wrong.

Answer:

We can rewrite 0.09 as \(\frac{9}{10^{2}}\) = 9×10^{-2} and rewrite 0.1 as \(\frac{1}{10^{1}}\) =1 ×10^{-1}. Because 0.09 has a smaller power of 10, 0.09 is closer to zero and is smaller than 0.1.