Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Module 2 Quiz Answer Key.

2.1 Scientific Notation with Positive Powers of 10

Write each number in scientific notation.

Question 1.
2,000 ______________
2,000 Given
2.0 Move the decimal point 3 places to the left. Remove the extra zeros.
1000 Divide the original number by the result from above.
103 Write the answer as power of 10.
2.0 × 103 Write the product of the results from the above.
2.0 × 103

Question 2.
91,007,500 ____________
91,007,500 Given
91,007,500 Move the decimal point 7 places to the left. Remove the extra zeros.
10000000 Divide the original number by the result from above.
107 Write the answer as power of 10.
9.10075 × 107 Write the product of the results from the above.
9.10075 × 107

Question 3.
On average, the Moon’s distance from Earth is about 384,400 km. What is this distance in scientific notation? __________________
Given that,
The average distance of the moon from the earth is 384,400 km.
The scientific notation of the distance 384400 is 3.844 x 10⁵.
Here move the decimal 5 times to the left then it is 3.844. But it is less than 10.
Moved the decimal to the left is the exponent and the exponent is positive.

Write each number in standard notation.

Question 4.
1.0395 × 109 _______________
1.0395 x 109 in the standard form is
109 = 1,000,000,000
1.0395 x 1,000,000,000 = 1,039,500,000.

Question 5.
4 × 102 _______________
4 x 10² in the standard form is
10² = 100
4 x 100 = 400

Question 6.
The population of Indonesia was about 2.48216 × 108 people in 2011. What is this number in standard notation? _______________
Given that the population of Indonesia is 2.48216 x 10⁸
2.48216 x 10⁸ in the standard form is
10⁸ = 100000000
2.48216 x 100000000 = 248,216,000

2.2 Scientific Notation with Negative Powers of 10

Write each number in scientific notation.

Question 7.
0.02 _______________
0.02 in the scientific notation is 2 x 10-2
Here move the decimal 2 times to the left then it is 2. But two is less than 10.
Moved the decimal to the left is the exponent and the exponent is negative.

Question 8.
0.000701 ____
0.000701 Given
7.01 Place the decimal point
4 Count the number of places the decimal point is moved
7.01 × 104 Multiply 7.01 times a power of 10. Since 0.000701 is less than 1, the decimal point moves to the right and the exponent on 10 is negative.

Write each number in standard notation.

Question 9.
8.9 × 10-5 ______________
8.9 × 10-5 Given
5 Use the exponent of the power of 10 to see how many places to move the decimal point.
places
0.000089 Place the decimal point Since you are going to write a number less than 8.9, move the decimal to the left. Add placeholder zeros if necessary.
0.000089

Question 10.
4.41 × 10-2 ______________
4.41 × 10-2 Given
2 Use the exponent of the power of 10 to see how many places to move the decimal point.
places
0.0441 Place the decimal point Since you are going to write a number less than 4.41, move the decimal to the left. Add placeholder zeros if necessary.
0.0441

Complete the table.

Question 11.

Given that,
The distance structure of the standard notation = 0.000009m.
0.000009m in the scientific notation is
The distance of the structure in the scientific notation is 9 x 10-6
Here move the decimal 6 times to the left then it is 9. But nine is less than 10.
Moved the decimal to the left is the exponent and the exponent is negative.

Question 12.

Given that,
The distance of the structure in the scientific notation is 9.5 x 10-9
9.5 x 10-9
10-9 = 0.000000009
9.5 x 0.000000009 = 0.0000000855
The distance structure of the standard notation = 0.0000000855

Question 13.

Given that,
The distance structure of the standard notation = 0.000009m.
0.000009m in the scientific notation is
The distance of the structure in the scientific notation is 9 x 10-6
Here move the decimal 6 times to the left then it is 9. But the nine is less than 10.
Moved the decimal to the left is the exponent and the exponent is negative.

Essential Question

Question 14.
How is scientific notation used in the real world?
Scientific notation is used to write very small and very large numbers using fewer digits.
It is used to describe the astronomical distances such as the distance between the cities and used in the microscopic distance means the length of blood cells.

Texas Go Math Grade 8 Module 2 Mixed Review Texas Test Prep Answer Key

Selected Response

Question 1.
Which of the following is the number 90 written in scientific notation?
(A) 90 × 102
(B) 9 × 102
(C) 90 × 101
(D) 9 × 101
The number 90 in the scientific notation is 9 × 101
Here move the decimal 1 times to the left then it is 9. But the nine is less than 10.
Moved the decimal to the left is the exponent and the exponent is positive.
Option D is the correct answer.

Question 2.
About 786,700,000 passengers traveled by plane in the United States in 2010. What is this number written in scientific notation?
(A) 7,867 × 105 passengers
(B) 7.867 × 102 passengers
(C) 7.867 × 108 passengers
(D) 7.867 × 109 passengers
(C) 7.867 × 108 passengers

Explanation:
786,700,000 Given
7.867 Move the decimal point 8 places to the left. Remove the extra zeros.
100000000 Divide the original number by the result from Step 1.
108 Write the answer as power of 10.
7.867 × 108 Write the product of the results from above
There are 7.867 × 108 passengers

Question 3.
In 2011, the population of Mali was about 1.584 × 107 people. What is this number written in standard notation?
(A) 1.584 people
(B) 1,584 people
(C) 15,840,000 people
(D) 158,400,000 people
(C) 15,840,000 people

Explanation:
1.584 × 107 Given
7 Use the exponent of the power of 10 to determine the number places to move the decimal point places

15,840,000 Place the decimal point. Since you are going to write a number greater than 1.584, move the decimal to the right. Add placeholder zeros if necessary.
There are
15,840,000 people

Question 4.
The square root of a number is between 7 and 8. Which could be the number?
(A) 72
(B) 83
(C) 51
(D) 66
(C) 51

Explanation:
7 and 8 Given

49 and Find the squares of the number
64
Since the square root lies between
$7$ and $8$, the square of the number
lies between $49$ and $64$, hence it
could be $51$

Question 5.
Pilar is writing a number in scientific notation. The number is greater than ten million and less than one hundred million. Which exponent will Pilar use?
(A) 10
(B) 7
(C) 6
(D) 2
The pilar is writing a number that number is in the scientific notation.
The number is greater than 1 million and less than 100 million.
1 million = 1000000 = 10⁶
100 million = 100000000 = 10⁸
Greater than 10⁶ and less than 10⁸
The exponent is 7,
Option B is the correct answer.

Question 6.
Place the numbers in order from least to greatest.
0.24, 4 × 10-2, 0.042, 2 × 10-4, 0.004
(A) 2 × 10-4, 4 × 10-2, 0.004, 0.042, 0.24
(B) 0.004, 2 × 10-4, 0.042, 4 × 10-2, 0.24
(C) 0.004, 2 × 10-4, 4 × 10-2, 0.042, 0.24
(D) 2 × 10-4, 0.004, 4 × 10-2, 0.042, 0.24
(D) 2 × 10-4, 0.004, 4 × 10-2, 0.042, 0.24

Explanation:
0.24, 4 × 10-2, 0.042, 2 × 10-4, 0.004
2.4 × 10-1 Express the numbers in scientific notation
4 × 10-2
4.2 × 10-2
2 × 10-4
4 × 10-3

2 × 10-4 Compare the power of 10 and if they are same
4 × 10-3 compare the first factor
4 × 10-2 Placed in the order from least to greatest
4.2 × 10-2
2.4 × 10-1
2 × 10-4, 0.004, 4 × 10-2, 0.042, 0.24 placed in the order from least to greatest

Question 7.
Which of the following is the number 1.0085 × 10-4 written in standard notation?
(A) 10,085
(B) 1.0085
(C) 0.00010085
(D) 0.000010085
1.0085 x 10-4 in the standard notation is
10-4 = 0.0001
1.0085 x 0.0001 = 0.00010085
Multiplying 1.0085 with 0.0001 then you get 0.00010085.
Option C is the correct answer.

Question 8.
A human hair has a width of about 6.5 × 10-5 meter. What is this width written in standard notation?
(A) 0.00000065 meter
(B) 0.0000065 meter
(C) 0.000065 meter
(D) 0.00065 meter
(C) 0.000065 meter

Explanation:
6.5 × 10-5 Given
5 Use the exponent of the power of 10 to see how many places to move the decimal point.
places
0.000065 Place the decimal point Since you are going to write a number less than 6.5, move the decimal to the left. Add placeholder zeros if necessary.
The width in standard notation is $0.000065$ meter

Gridded Response

Question 9.
Write 2.38 × 10-1 in standard form.