Into Math Grade 8 Module 12 Answer Key Exponents and Scientific Notations

We included HMH Into Math Grade 8 Answer Key PDF Module 12 Exponents and Scientific Notations to make students experts in learning maths.

HMH Into Math Grade 8 Module 12 Answer Key Exponents and Scientific Notations

Exponents, Scientific Notation, and Volume

Cosmologist
People who lived 600 years ago believed the sun, the planets, and the stars revolved around Earth, which was thought to be at the center of the universe. Today, we know this is not true thanks to discoveries by cosmologists, scientists who study the origin and evolution of the universe. Cosmologists are curious about the universe and sometimes work for decades to solve problems related to it.

STEM Task:

Light travels at a speed of about 186,000 miles per second in a vacuum. About how many miles does light travel in one hour? Write your answer in standard form and as a number multiplied by a power of 10.

Learning Mindset Strategic Help-Seeking Identifies Need for Help

It is impossible to know the exact number of people who worked to develop all of the technology required to send spacecraft to the moon. But it is reasonable to estimate that hundreds of thousands of people from universities, government, and industry contributed, and continue to contribute to the task.
No one could have done such a complex task alone. People had to collaborate with and help each other. Remember that when you need to ask for help. Here are some tips on when, where, and how to seek help strategically.

• Try to solve a problem three ways before you ask another person for help. Identify resources such as books or videos you could use to solve the problem.
• When you seek help from others, describe exactly what you understand about the problem and what you do not understand. Be as clear and specific as you can.

Reflect

Question 1.
Were you able to work through the challenges of the STEM Task on your own, or did you need help from another person? How did you know you needed help?
Answer:

Question 2.
What resources did you use to complete the STEM Task?
Answer:

A-Mazing Expressions

Find a path through the maze by evaluating each of the expressions shown. You can move from one space to the next only if the value of the expression in the space you are in is less than the value of the expression in the space you are moving to. You can move left, right, up, or down, but not diagonally.

Answer:

Turn and Talk

Explain how to determine whether you can move from 2.46 × 10² to 6.74 × 10³ without performing any operations.
Answer:
2.46 × 10² = 2.46 × 10 × 10 = 246
6.74 × 10³ = 6.74 × 10 × 10 × 10 = 6740

Are You Ready?

Complete these problems to review prior concepts and skills you will need for this module.

Order of Operations

For Problems 1-8, determine the value of each expression.

Question 1.
36 × 10⁵ __________
Answer:
36 × 10⁵ = 36 × 10 × 10 × 10 × 10 × 10 = 3,600,000

Question 2.
1.24 × 10⁴ _____________
Answer:
1.24 × 10⁴ = 1.24 × 10 × 10 × 10 × 10 = 12,400

Question 3.
179 ÷ 10³ ____________
Answer:
179 ÷ 10³ = 179 ÷ 1000 = 0.179

Question 4.
1.5 ÷ 10² ____________
Answer:
1.5 ÷ 10² = 1.5 ÷ 100 = 0.015

Question 5.
(3.5 × 10³) + (4.27 × 10³) _____________
Answer:
(3.5 × 10³) + (4.27 × 10³)
(3.5 × 10 × 10 × 10) + (4.27 × 10 × 10 × 10)
3500 + 4270 = 7770

Question 6.
(6.7 × 10⁴) – (5.82 × 10²) ____________
Answer:
(6.7 × 10⁴) – (5.82 × 10²)
(6.7 × 10 × 10 × 10 × 10) – (5.82 × 10 × 10)
67000 – 582 = 66418

Question 7.
(8.3 × 10³) × (9.71 × 10²) _____________
Answer:
(8.3 × 10³) × (9.71 × 10²)
(8.3 × 10 × 10 × 10) × (9.71 × 10 × 10)
8300 × 971 = 8,059,300

Question 8.
(5.52 × 10²) ÷ (4.6 × 10³) _____________
Answer:
(5.52 × 10²) ÷ (4.6 × 10³)
(5.52 × 10 × 10) ÷ (4.6 × 10 × 10 × 10)
552 ÷ 4600 = 0.12

Solve Multi-Step Problems

Question 9.
At a grocery store, sliced turkey from the deli counter costs $7.92 per pound. A customer purchases 0.625 pound of sliced turkey. Excluding tax, how much change will she receive if she pays with a $20 bill?
$ ___________
Answer:
Given,
At a grocery store, sliced turkey from the deli counter costs $7.92 per pound.
A customer purchases 0.625 pound of sliced turkey.
1 lb = $7.92
0.625 lb = x
x = 7.92 × 0.625
x = $4.95
She gave $20
$20 – $4.95 = $15.05
Thus she will receive $15.05 change.

Question 10.
It takes Steven 12.25 minutes to run 1.4 miles. At this rate, how long will it take him to run 2.6 miles?
____________ minutes
Answer:
Given,
It takes Steven 12.25 minutes to run 1.4 miles.
To find:
how long will it take him to run 2.6 miles?
2.6 × 12.25 ÷ 1.4
(2.6 × 12.25)/1.4 = 22.75 minutes
Thus it takes 22.75 minutes for him to run 2.6 miles.

Question 11.
An account with $600 earns 4% simple interest per year. The next year all the money is put into a new account that earns 4.5% simple interest per year. How much money does the account have at the end of the second year? Explain.
Answer:
Given,
An account with $600 earns 4% simple interest per year.
600 × 0.04 × 1 = 24 × 1 = $24
The next year all the money is put into a new account that earns 4.5% simple interest per year.
600 × 0.045 × 1 = 27 × 1 = $27
24 + 27 = $51

Question 12.
Anthony has two cube-shaped pots with an interior edge length of 8 inches and two cube-shaped pots with an interior edge length of 6.5 inches. He wants to fill each pot full of potting soil. His bag of potting soil is one cubic foot. How much soil will he have left after he fills each pot full of soil?
Answer:
Given,
Anthony has two cube-shaped pots with an interior edge length of 8 inches.
He wants to fill each pot full of potting soil. His bag of potting soil is one cubic foot.
We know that,
Volume of a cube = s³
1 foot = 12 inches
s = 8
V = 8 × 8 × 8 = 512 cubic. inches
He has another two cube-shaped pots with an interior edge
length of 6.5 inches
V = 6.5 × 6.5 × 6.5 = 274.625 cu. inches
Volume of two pots = 274.625 × 2 = 549.25 cu. inches
He wants to fill each pot full of potting soil.
The volume of soil he uses to fill the 4 pots is equal to the volume of the four pots.
Total volume = 1024 + 549.25 = 1573.25 cu. in
The total soil he uses = 1573.25 cu. in
His bag of potting soil is one cubic foot.
1 cubic feet = 1728 cubic inches
The soil he will left = 1728 – 1573.25 = 154.75 cu. inches
Therefore he has 154.75 cu. inches after he sills each pot full of soil.