Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation

We included HMH Into Math Grade 8 Answer Key PDF Module 12 Lesson 3 Compute with Scientific Notation to make students experts in learning maths.

HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation

I Can compute with scientific notation, choose appropriate units for real-world quantities, and convert values in scientific notation from one unit to another.

Step It Out

Question 1.
You can add and subtract with scientific notation to analyze the data in the table.
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 1
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 2
A. How many more people visited Grand Canyon National Park than Yellowstone National Park?
To add or subtract with scientific notation, first express the quantities with the same power of 10. These data have the same power of 10.
Use the Distributive Property:
5.97 × 106 – 4.26 × 106 = (5.97 – 4.26) × 106
Subtract the first factors: 5.97 – ___________ = ____________
Express the difference with the same power of 10.
___________ × 106 more people, or more people, visited Grand Canyon National Park than Yellowstone National Park.
Answer:
To add or subtract with scientific notation, first, express the quantities with the same power of 10. These data have the same power of 10.
Use the Distributive Property:
5.97 × 106 – 4.26 × 106 = (5.97 – 4.26) × 106
Subtract the first factors: 5.97 – 4.26 = 1.71
Express the difference with the same power of 10.
1.71 × 106 more people, or more people, visited Grand Canyon National Park than Yellowstone National Park.

B. What was the total number of visitors to Great Smoky Mountains National Park and Grand Canyon National Park?

Since the numbers are written with different powers of 10, we need to rewrite one number so they have the same power of 10. To do this, multiply the first factor by 10 and divide the power of 10 by 10.
1.13 × 107 = (1.13 × 10) × (107 ÷ 10) = _________ × ___________
Now add the first factors: ___________ + __________ = ____________
Express the sum with the same power of 10: ___________ × 106.
To write your answer in scientific notation, determine how to write the first factor as a number between 1 and 10. In this case, divide 17.27 by 10. To keep the value the same, multiply 106 by 10 to get 107.
__________ × 106 = __________ × 107
Answer:
Since the numbers are written with different powers of 10, we need to rewrite one number so they have the same power of 10. To do this, multiply the first factor by 10 and divide the power of 10 by 10.
1.13 × 107 = (1.13 × 10) × (107 ÷ 10) = 11.3 × 107
Now add the first factors: 11.3 + 5.97 = 17.27
Express the sum with the same power of 10: 17.27 × 106 .
To write your answer in scientific notation, determine how to write the first factor as a number between 1 and 10. In this case, divide 17.27 by 10. To keep the value the same, multiply 106 by 10 to get 107.
17.27 × 106 = 1727 × 107

Turn and Talk How could you solve the problem in Part B by rewriting the quantity for the Grand Canyon rather than the Great Smoky Mountains?
Answer:

Question 2.
Mammoth Cave National Park in Kentucky is known for its limestone stalactites, which form very slowly. About how much does a stalactite grow in 500 years?
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 3
A. Express 500 years in scientific notation.
500 years = ___________ × ___________ years
Answer:
To change 500 into the scientific notation move the decimal two places to the left. So in the left place, there are only 5. And the number 2 indicates the exponent of 10.
500 years in scientific notation is 5 x 10²

B. Multiply to find the total amount of growth for the stalactite in 500 years.
When you multiply or divide in scientific notation, multiply or divide the first factors by each other and multiply or divide the powers of 10 by each other.
(3.3 × 10-4) × (_________ × __________)
= (3.3 × __________) × (10-4 × __________)
= ____________ × ____________
Answer:
When you multiply or divide in scientific notation, multiply or divide the first factors by each other and multiply or divide the powers of 10.
(3.3 × 10-4) × (5 x 10²)
= (3.3 × 5) × (10-4 × 10²)
The total amount of growth for the stalactite in 500 years. = 16.5 × 10-2

C. Express the product using scientific notation. Rewrite the product so that the first factor is greater than or equal to 1 but less than 10.
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 4
Express the approximate amount of growth in 500 years in scientific notation and in standard form.
Answer:
Given that,
The product’s first factor is greater than or equal to 1 but less than 10 is 1.927 x 104
1.927 x 104 in scientific notation is 1.927 x 104

The approximate growth for the stalactite in 500 years. = 16.5 × 10-2
16.5 × 10-2 in scientific notation is 1.65 × 10-1
16.5 × 10-2 in standard form is 0.165.

D. In Part B, which property of multiplication allows you to change the order of the factors, and which property allows you to regroup the factors so that you can multiply the first factors together and multiply the powers of 10 together?
Answer:
You can use the Distributive Property of multiplication to change the order of the factors and regroup the factors.
So, you can multiply the first factors together and then multiply the powers of 10 together.

E. In Part B, what property of exponents makes it easy to multiply the powers of 10? Explain.
Answer:
The property of exponents makes it easy to multiply the powers of 10 is multiplying the two exponents when the bases are equal then the powers sound be added.

Turn and Talk In Part C, what unit of measure would be more appropriate to express the amount of growth than feet? Express the amount of growth using the measure you named.

Question 3.
The table shows the areas of three national parks. Find the total area of the parks. Write the total area using scientific notation and a more appropriate unit of measure.
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 5
A. Write the area of Everglades National Park in scientific notation.
6,100,000,000 m2 = __________ × __________ m2
Answer:
The area of Everglades National Park is 6,100,000,000 m2
6,100,000,000 m2 in scientific notation is 6.1 x 109

B. Many calculators have a key labeled EE or 10x that allows you to enter values in scientific notation. The display may look like scientific notation with the “x 10” replaced.
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 6
Use a calculator to add the three areas. Write the sum as it appears on your calculator. Then write it in scientific notation.
Answer:
Given that,
The area of Death Valley = 1.4 x 1010
The area of Everglades National Park is 6,100,000,000 m2 = 6.1 x 109
The area of the Glacier = 4.1 x 109
The total sum of three areas is (1.4 x 1010) + (6.1 x 109) + (4.1 x 109)
The sum as it appears on your calculator is 11.6 x 1028
11.6 x 1028 in scientific notation is 1.16 x 1029 m2

C. You found the total area of the three national parks in square meters. Square kilometers is a more appropriate unit for a large area.

There are 1000 or 103 meters in 1 kilometer. So, there are 103 × 103 = 106 square meters in 1 square kilometer. Divide your result from Part B by 106 to express the total area in square kilometers.
____________ × ____________ ÷ 106 = ____________ × ___________
The total area of the national parks is __________ × ____________ square kilometers.
Answer:
There are 1000 or 103 meters in 1 kilometer. So, there are 103 × 103 = 106 square meters in 1 square kilometer. Divide your result from Part B by 106 to express the total area in square kilometers.
1.16 x 1029 ÷ 106 = 1.16 x 1023
The total area of the national parks is 1.16 x 1023 square kilometers.

Turn and Talk How would you convert from square kilometers to square meters?
Answer:
To convert from square kilometers to square meters. Multiply the area by the conversion ratio and the area in the square meters is equal to the square kilometers multiplied by 1,000,000.

Check Understanding

Question 1.
One library has 4.1 × 105 books. A second library has 6,200,000 books. Find the total number of books at the two libraries using scientific notation.
Answer:
Given that,
The total number of books in the first library is 4.1 × 105 books.
The total number of books in the second library is 6,200,000 books = 6.2 x 106
The total number of books = (4.1 × 105) + (6.2 x 106)
= 10.3 x 1011
10.3 x 1011 in scientific notation is 1.03 x 1012

Add or subtract. Express your answer in scientific notation.

Question 2.
(5.7 × 108) + (3.2 × 106)
Answer:
Given that,
(5.7 × 108) + (3.2 × 106)
Here the bases are equal then the powers should be added.
= (5.7 + 3.2) x (108 + 106)
= 8.9 x (108+6)
= 8.9 x 1014
8.9 x 1014 in scientific notation is 0.89 x 1015

Question 3.
(1.3 × 10-4) – (7.5 × 10-5)
Answer:
Given that,
(1.3 × 10-4) – (7.5 × 10-5)
Change 10-5 to 10-4
Move the decimal on 7.5 to the left by one place than 7.5 = 0.75
= (1.3 – 0.75) x 10-4
= 0.55 x 10-4
0.55 x 10-4 in scientific notation is 5.5 x 10-5

Multiply or divide. Express your answer in scientific notation.

Question 4.
(2.8 × 107) × ( 3.5 × 10-3)
Answer:
Given that,
(2.8 × 107) × (3.5 × 10-3)
Multiply the coefficients and powers of ten separately then combine and add exponents in multiplication.
= (2.8 x 3.5) x (107× 10-3)
= 9.8 x (107+(-3))
= 9.8 x (104)
9.8 x (104) in scientific notation is 9.8 x 104

Question 5.
(7.2 × 1012) ÷ (3 × 105)
Answer:
Given that,
(7.2 × 1012) ÷ (3 × 105)
Divide the coefficients and powers of ten separately then combine and subtract exponents in the division.
= (7.2/3) x (1012)/ (105)
= 2.4 x 1012-5
= 2.4 x 107
=  2.4 x 107 in scientific notation is 2.4 x 107

On Your Own

For Problems 6-8, use the data shown about the average number of vehicles per day crossing each bridge. Express your answers in scientific notation.
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 7

Question 6.
Find the total average number of vehicles per day crossing the bridges.
Answer:
Given that,
The total number of vehicles crossing the Golden gate bridge per day = 112,000.
The total number of vehicles crossing the San Francisco- Oakland Bay Bridge = 2.7 x 107
112,000 = 1.12 x 102
The total average number of vehicles per day crossing the bridges = (1.12 x 102) + (2.7 x 107)
= (1.12 + 2.7) x (102 x 107)
= 3.82 x 109
= 3.82 x 109 in scientific notation is 3.82 x 109

Question 7.
How many more vehicles cross the San Francisco-Oakland Bay Bridge each day than the Golden Gate Bridge, on average?
Answer:
Given that,
The total number of vehicles crossing the Golden gate bridge per day = 112,000.
The total number of vehicles crossing the San Francisco- Oakland Bay Bridge = 2.7 x 107
112,000 = 1.12 x 102
The vehicles cross the San Francisco-Oakland Bay Bridge each day than the Golden Gate Bridge = (2.7 x 107) – (1.12 x 102)
2.7 x 107 in standard form is 27,000,000
1.12 x 102 in standard form is 112
Therefore 27,000,000 – 112 = 26,999,888
26,999,888 in the scientific notation is 2.6,999,888 x 104

Question 8.
Use Structure What is the average number of vehicles that cross each bridge in one year?
Answer:
Given that,
The average number of vehicles crossing the Golden gate bridge per day = 112,000 = 1.12 x 102
The average number of vehicles crossing the San Francisco- Oakland Bay Bridge = 2.7 x 107

For Problems 9-11, use the table shown.
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 8
Question 9.
What is the total population of the four cities shown in the table? Express your answer in scientific notation and in standard form.
Answer:
Given that,
The population in the Houston = 2.3 x 106
The population in the San Antonio = is 1.5 x 106
The population in the El paso = 6,80,000 = 6.8 x 105
The population in the Corpus Christo = 3.2 x 105
The total population of four cities is (2.3 x 106) + (1.5 x 106) + (6.8 x 105) + (3.2 x 105)
= (2.3 + 1.5 + 6.8 + 3.2) x (106 +106+105+ 105)
= 13.8 x 1022
13.8 x 1022 in scientific notation is 1.38 x 1023
In standard form is 138,000,000,000,000,000,000,000.

Question 10.
About how many more people live in Houston than in El Paso? Express your answer in scientific notation.
Answer:
Given that,
The population in the Houston = 2.3 x 106
The population in the El paso = 6,80,000 = 6.8 x 105
2.3 x 106 in standard form is2,300,000
6.8 x 105 in standard form is 680,000
The number of people live in Houston than in El Paso is 2,300,000 – 680,000 = 1,620,000
1,620,000 in scientific notation is 1.62 x 106

Question 11.
About how many times as many people live in El Paso as in Corpus Christi?
Answer:
Given that,
The population in the El paso = 6,80,000 = 6.8 x 105
The population in the Corpus Christo = 3.2 x 105
The number of people living in EI Paso as in Corpus Christi is (6.8 x 105) – (3.2 x 105)
= (6.8 – 3.2) x 105
= 3.6 x 105 in scientific notation is 3.6 x 105
Therefore the number of people living in EI Paso as in Corpus Christi is 3.6 x 105

Question 12.
STEM A typical Escherichia coil (or E. coi,) bacterial cell is about 7.9 × 10-5 inch long. Suppose you could line up E. coil cells, end to end, across a Petri dish with a diameter of 2 inches. About how many cells would fit across the dish? Explain your method.
Answer:

For Problems 13-14, a ream of paper contains 500 sheets and a case of paper contains 10 reams.

Question 13.
An office supply store gets a delivery of 400 cases. How many sheets of paper are in the delivery? Express your answer in scientific notation.
Answer:
Given that,
An office supply store gets a delivery of 400 cases
1 case = 10 reams
400 cases = 400 x 10 = 4000 reams
1 ream = 500 sheets
4000 reams = 4000 x 500 = 2,000,000 sheets.
2,000,000 sheets in scientific notation is 2 x 106

Question 14.
Use Tools A ream of paper is 4.5 × 10-2 meter thick. Use a calculator to find the thickness of a single sheet of paper. Then express the answer using a more appropriate unit of length.
Answer:
Given that,
A ream of paper is 4.5 × 10-2 meter thick
1 ream = 500 sheets
The thickness of one sheet is 4.5 × 10-2/500
= 0.045/500
= 0.00009 meters
Therefore the thickness of one sheet is 0.00009 meters

For Problems 15-16, the image shows the top speed at which a Galapagos tortoise can travel.

HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 9

Question 15.
At its top speed, how far does the tortoise travel in one minute? Use an appropriate unit of length for your answer.
Answer:
Given that,
The speed of a tortoise is 3 x 10-1km/hr.
How far tortoises travel in one minute is
1 hour 60 minutes.
1 minute = 3 x 10-1/60.
= 0.3/60
= 0.005
0.005 in the scientific notation is 5 x 10-3
The tortoise’s travel in one minute is 5 x 10-3km/min.

Question 16.
The top speed of a cheetah is 1.2 × 102 kilometers per hour. How many times as fast is the cheetah as the tortoise?
Answer:

Given that,
The speed of a cheetah is 1.2 × 102kilometres per hour.
The speed of a tortoise is 3 x 10-1km/hr.
The number of times as fast as the cheetah as the tortoise is (1.2 × 102) – (3 x 10-1)
1.2 × 102 = 120
3 x 10-1 =0.3
Therefor 120 – 0.3 = 119.7.
119.7 in scientific notation is 1.197 x 102
The number of times as fast is the cheetah as the tortoise is 1.197 x 102

Question 17.
Open-Ended Write two numbers in scientific notation so that all of the following are true.

  • Both numbers are greater than 1 × 102.
  • Both numbers are less than 1 × 106.
  • The product of the two numbers is 5 × 106.

Then use a calculator to verify the product of the two numbers.
Answer:

Question 18.
Reason New Zealand consists of hundreds of islands. Most of the population lives on the North Island, which has an area of 1.14 × 105 square kilometers, and the South Island, which has an area of 151,000 square kilometers.
A. Which island has a greater area? How many square kilometers greater is it? Express your answer in scientific notation.
Answer:
Given that,
The population lives on the North Island, which has an area of 1.14 × 105 square kilometres.
The population lives on the South Island, which has an area of 151,000 square kilometers.
151,000 = 1.51 x 105
The South Island has the greater population.
= (1.51 x 105) – (1.14 × 105)
= 0.37 × 105
The South Island is 0.37 × 105 greater than the North Island.
0.37 × 105 in scientific notation is 3.7 × 104 square kilometers

B. The population of the North Island and South Island combined is about 4.8 × 106. Find the approximate population density in people per square kilometer, rounded to the nearest unit. Explain your steps.
Answer:

Question 19.
About how many sesame seeds are in one gram of sesame seeds?
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 10
Answer:

Given that,
A single sesame seed weighs approximately 4 x 10-6
1 kilogram = 1000 grams.
Sesame seed per 1 gram = 4 x 10-6/1000
= 0.000004/1000
= 0.000000004
= 4 x 10-9 grams
Sesame seed per 1 gram = 4 x 10-9 grams.
4 x 10-9 grams in scientific notation is 4 x 10-9 grams.

Question 20.
Use Structure Marisol multiplies 3 × 10-2 and 4 × 10-5 and gets 12 × 10-7as the product. What steps should she take next to write the product using correct scientific notation? Explain why these steps will not change the value of the product.
Answer:

For Problems 21-24, add or subtract. Express your answer in scientific notation.

Question 21.
(1.4 × 105) + (9.5 × 10-6)
Answer:
Given that,
(1.4 × 105) + (9.5 × 10-6)
= (1.4 + 9.5) x (105 + 10-6)
If bases are equal then the powers should be added.
= 10.9 x 10-1
10.9 x 10-1 in scientific notation is 1.09 x 100

Question 22.
(4.7 × 1010) – (6.8 × 109)
Answer:
Given that,
(4.7 × 1010) – (6.8 × 109)
Convert 1010 to 109
Move the decimal on 6.8 to the left by one place then 6.8 = 0.68
= (4.7 + 0.68) x 109
= 5.38 x 109
5.38 x 109 in scientific notation is 5.38 x 109

Question 23.
(4.4 × 106) + (7.1 × 106)
Answer:
Given that,
(4.4 × 106) + (7.1 × 106)
= (4.4 + 7.1) x (106 +106)
If bases are equal then the powers should be added.
= 11.5 x 1012
11.5 x 1012 in scientific notation is 1.15 x 1013

Question 24.
(8.5 × 10-2) – (8.5 × 10-3)
Answer:
Given that,
(8.5 × 10-2) – (8.5 × 10-3)
Convert 10-3 to 10-2
Move the decimal on 8.5 to the left by one place than 8.5 = 0.85
= (8.5 – 0.85) x 10-2
= 7.65 x 10-2
(8.5 × 10-2) – (8.5 × 10-3) in the scientific notation is 7.65 x 10-2

For Problems 25-28, multiply or divide. Express your answer in scientific notation.

Question 25.
(1.8 × 103) × (2.25 × 105)
Answer:
Given that,
(1.8 × 103) × (2.25 × 105)
Multiply the coefficients and powers of ten separately then combine and add exponents in multiplication.
= (1.8 x 2.25) x (103× 105)
= 4.05 x 103+5
= 4.05 x 108
(1.8 × 103) × (2.25 × 105) in the scientific notation is 4.05 x 108

Question 26.
(6 × 10-8) ÷ (1.5 × 10-9)
Answer:
Given that,
(6 × 10-8) ÷ (1.5 × 10-9)
Divide the coefficients and powers of ten separately then combine and subtract exponents in the division.
= (6/1.5) x (10-8)/ (10-9)
= 4 x 101
(6 × 10-8) ÷ (1.5 × 10-9) in scientific notation is 4 x 101

Question 27.
(8.2 × 10-7) × (3.1 × 1011)
Answer:
Given that,
(8.2 × 10-7) × (3.1 × 1011)
Multiply the coefficients and powers of ten separately then combine and add exponents in multiplication.
= (8.2 x 3.1) x (10-7× 1011)
= 25.42 x 104
(8.2 × 10-7) × (3.1 × 1011) = 25.42 x 104
25.42 x 104 in scientific notation is 2.542 x 105

Question 28.
(9.6 × 105) ÷ (3 × 105)
Answer:
Given that,
(9.6 × 105) ÷ (3 × 105)
Divide the coefficients and powers of ten separately then combine and subtract exponents in the division.
= 9.6/3 x (105)/ (105)
= 3.2 x 100
(9.6 × 105) ÷ (3 × 105) in scientific notation is 3.2 x 100

Question 29.
Critique Reasoning Tim was asked to find the difference of 5.9 × 107 and 2.4 × 107. His work is shown here. Did he find the difference correctly? If so, name the mathematical properties he used. If not, explain his error and find the correct difference.
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 11
Answer:
Given that,
Tim was asked to find the difference between 5.9 × 107 and 2.4 × 107.
His work is wrong because he didn’t subtract the second term.
The correct answer is
(5.9 × 107) – (2.4 × 107)
= (5.9 – 2.4) x 107
= 3.5 x 107
The correct answer is 3.5 x 107

Lesson 12.3 More Practice/Homework

Question 1.
School District A has 5.6 × 105 students. School District B has 2.5 × 105 students. What is the total number of students in the two school districts?
Answer:
Given that,
School District A has 5.6 × 105 students.
School District B has 2.5 × 105 students.
The total sum of the two school districts = (5.6 × 105) + (2.5 × 105)
= (5.6 + 2.5) x (105+105)
= 8.1 x 1010
The total sum of the two school districts = 8.1 x 1010

The mass of a typical aphid is shown in the photo. The mass of a typical worker ant is 3 × 10-6 kilogram. Use this information to answer Problems 2-3 Use a calculator to verify your answers.
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 12

Question 2.
What is the combined mass of an aphid and a worker ant?
Answer:
Given that,
The mass of a typical aphid is 2 x 10-7 kilogram.
The mass of a typical worker ant is 3 × 10-6 kilogram.
The combined mass of an aphid and a worker ant is (2 x 10-7) + (3 × 10-6)
= (2 + 3) x (10-7+10-6)
= 5 x 10-13 kilogram.
The combined mass of an aphid and a worker ant is 5 x 10-13 kilogram.

Question 3.
How much greater is the mass of a worker ant than the mass of an aphid?
Answer:
Given that,
The mass of a typical worker ant is 3 × 10-6 kilogram.
The mass of a typical aphid is 2 x 10-7 kilogram.
The mass of a typical worker ant greater than typical aphid is (3 × 10-6) – (2 x 10-7)
(3 × 10-6) in standard form is 0.0000003
(2 x 10-7) in standard form is 0.00000002
The mass of a typical worker ant greater than a typical aphid is 0.0000003 – 0.00000002 = 0.00000028
0.00000028 in the scientific notation is 2.8 x 10-7

Question 4.
Attend to Precision A factory produces boxes of paper clips that each contain 2.5 × 102 paper clips. Every hour, the factory produces 8000 boxes. Assuming the factory operates 24 hours per day, how many paper clips are produced in one week? Express your answer in scientific notation.
Answer:
Given that,
A factory produces boxes of paper clips.
Each box contains 2.5 × 102 paper clips.
The number of boxes is 8000 per 1 hour.
The factory operates 24 hours per day
1 week = 7 days
1 day = 24 hours
1 week = 7 x 24 = 168 hours.
Number of boxes per 168 hours = 8000 x 168 = 1,344,000.
The number of paper clips = 1,344,000 x 2.5 × 102 = 336,000,000.
336,000,000 in scientific notation is 3.36 x 108

Question 5.
Math on the Spot The table shows the approximate surface areas for three oceans given in square meters. What is the total surface area of these three oceans? Write the answer in scientific notation using more appropriate units.
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 13
Answer:
Given that,
The total surface area of the Atlantic is 7.68 x 1013
The total surface area of the Indian is 6.86 x 1013
The total surface area of the Arctic is 1.41 x 1013
The total surface area of all three oceans is (7.68 x 1013) + (6.86 x 1013) + (1.41 x 1013)
= (7.68 + 6.86 + 1.41) x (1013 + 1013 + 1013)
= 15.95 x 1039
15.95 x 1039 in scientific notation is1.595 x 1040

Add or subtract. Express your answer in scientific notation.

Question 6.
(7.7 × 106) – (2.5 × 106)
Answer:
Given that,
(7.7 × 106) – (2.5 × 106)
(7.7 × 106) in standard form is 7,700,000
(2.5 × 106) in standard form is 2,500,000
7,700,000 – 2,500,000 = 5,200,000
5,200,000 in scientific notation is 5.2 x 106

Question 7.
(3.9 × 104) + (7.5 × 105)
Answer:
Given that,
(3.9 × 104) + (7.5 × 105)
Here the bases are equal then the powers should be added.
= (3.9 + 7.5) x 104+5
= 11.4 x 109
11.4 x 109 in scientific notation is = 1.14 x 1010

Question 8.
(5.22 × 10-2) + (3.85 × 10-3)
Answer:
Given that,
(5.22 × 10-2) + (3.85 × 10-3)
Here the bases are equal then the powers should be added.
= (5.22 + 3.85) x (10-2 + 10-3)
= 9.07 x (10-2+(-3))
= 9.07 x 10-5
9.07 x 10-5
9.07 x 10-5 in scientific notation is 9.07 x 10-5

Question 9.
(1.4 × 10-7) – (4.4 × 10-8)
Answer:
Given that,
(1.4 × 10-7) – (4.4 × 10-8)
Convert 10-8 to 10-7
In 4.4 move one decimal to the left then it is 0.44 x 10-7
(1.4 × 10-7) – (0.44 x 10-7)
= (1.4 – 0.44) x 10-7
= 0.96 x 10-7
0.96 x 10-7 in scientific notation is 9.6 x 10-7

Multiply or divide. Express your answer in scientific notation.

Question 10.
(7.2 × 104) × (1.8 × 103)
Answer:
Given that,
(7.2 × 104) × (1.8 × 103)
Multiply the coefficients and powers of ten separately then combine and add exponents in multiplication.
= (7.2 x 1.8) x (104 x 103)
= 12.96 x 104+3
= 12.96 x 107
(7.2 × 104) × (1.8 × 103) = 12.96 x 107
12.96 x 107 in scientific notation is 1.269 x 108

Question 11.
(8.4 × 10-5) ÷ (4.2 × 10-6)
Answer:
Given that,
(8.4 × 10-5) ÷ (4.2 × 10-6)
Divide the coefficients and powers of ten separately then combine and subtract exponents in the division.
(8.4 × 10-5)/ (4.2 × 10-6) = 8.4/4.2 x (10-5)/ (10-6).
= 2 x 101
(8.4 × 10-5) ÷ (4.2 × 10-6) = 2 x 101
2 x 101 in scientific notation is 2 x 101

Question 12.
(4.1 × 1012) × (3.5 × 10-7)
Answer:
Given that,
(4.1 × 1012) × (3.5 × 10-7)
Multiply the coefficients and powers of ten separately then combine and add exponents in multiplication.
(4.1 x 3.5) x (1012 x 10-7)
= 14.35 x 105
(4.1 × 1012) × (3.5 × 10-7) = 14.35 x 105
14.35 x 105 in scientific notation is 1.435 x 106

Question 13.
(5.2 × 10-3) ÷ (4 × 106)
Answer:
Given that,
(5.2 × 10-3) ÷ (4 × 106)
Divide the coefficients and powers of ten separately then combine and subtract exponents in the division.
= 5.2/4 x (10-3)/ (106)
= 1.3 x 103
(5.2 × 10-3) ÷ (4 × 106) = 1.3 x 103
1.3 x 103 in the scientific notation is 1.3 x 103

Test Prep

Question 14.
Draw a line to match each expression with its correct value.
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 14
Answer:
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation_14
The table shows the total seasonal attendance for four soccer teams. Use the table to answer Problems 15-17.

HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 15

Question 15.
What was the combined seasonal attendance for the Aviators and the Wranglers?
(A) 2.46 × 104 attendees
(B) 3.9 × 104 attendees
(C) 3.68 × 108 attendees
D) 3.9 × 108 attendees
Answer:
Given that,
The seasonal attendance of the Aviators = 2.3 x 104.
The seasonal attendance of the Wranglers = 16000.
16000 = 1.6 x 104
The combined seasonal attendance for the Aviators and the Wranglers = 2.3 x 104 + 1.6 x 104
= (2.3 + 1.6) x 108
= 3.9 x 108
Option D is the correct answer.

Question 16.
How much greater was the Wranglers’ seasonal attendance than the Barracudas’ seasonal attendance? Write your answer in scientific notation.
Answer:
Given that,
The seasonal attendance of the Wranglers = 16000.
The seasonal attendance of the Barracudas = 8.9 x 103
16000 = 1.6 x 104
Therefore 1.6 x 10– 8.9 x 103
1.6 x 104 in standard form is 16,000
8.9 x 103 in standard form is 8,900
Therefore 16,000 – 8,900 = 7100
7000 in scientific notation is 7.1 x 103

Question 17.
The Aviators’ season consisted of 8 games. What was the average attendance per game? Express your answer in scientific notation and in standard form.
Answer:
Given that,
The seasonal attendance of the Aviators = 2.3 x 104.
The Aviators’ season consisted of 8 games.
The average attendance per game was 2.3 x 104/8
= 23,000/8
= 2,875
2,875 in the scientific notation is 2.875 x 103

Spiral Review

Question 18.
Ava wants to use △PQR to prove the Pythagorean Theorem. She draws \(\overline{Q T}\) as shown. She starts her proof by identifying three similar triangles in the figure and writing proportions based on their side lengths. Complete the proportions.
HMH Into Math Grade 8 Module 12 Lesson 3 Answer Key Compute with Scientific Notation 16
Answer:
The proportions based on their side lengths of the Pythagorean Theorem is
QR/TR = PR/QP
QP/TP = PR/QR

Question 19.
Use the Pythagorean Theorem to find the distance between the points (2, 3) and (-1, -2). Round to the nearest tenth.
Answer:
Given that,
The points are (x1, y1) = (2, 3)
(x2, y2) = (-1, -2)
The formula for the Distance of the Pythagorean theorem is d = sqrt (x2 – x1)2  + (y2 – y1)2
= (-1 – 2)2 + (-2 – 3)2
= (9) + (25)
= 34 km
34 rounded to the nearest tenth is 30 km.

Question 20.
Order the values from least to greatest: (3 + \(\sqrt {5}\) ), π, \(\frac{5}{2}\), (6 + \(\sqrt {2}\) ), –\(\sqrt {16}\) .
Answer:
Given that,
(3 + \(\sqrt {5}\) ) = 3 + sqrt(5) = 5.236
π = 3.14
\(\frac{5}{2}\) = 5/2 = 2.5
(6 + \(\sqrt {2}\) ) = 6 + sqrt(2) = 7.414
–\(\sqrt {16}\) = -sqrt(16) = -4
The order of values from the least to greatest is –\(\sqrt {16}\) = -sqrt(16) = -4, \(\frac{5}{2}\), π, (3 + \(\sqrt {5}\) ), (6 + \(\sqrt {2}\) ) = 6 + sqrt(2).

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