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## Texas Go Math Grade 8 Module 2 Quiz Answer Key

**Texas Go Math Grade 8 Module 2 Ready to Go On? Answer Key**

**2.1 Scientific Notation with Positive Powers of 10**

**Write each number in scientific notation.**

Question 1.

2,000 ______________

Answer:

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.

10^{3} Write the answer as power of 10.

2.0 × 10^{3} Write the product of the results from the above.

2.0 × 10^{3}

Question 2.

91,007,500 ____________

Answer:

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.

10^{7} Write the answer as power of 10.

9.10075 × 10^{7} Write the product of the results from the above.

9.10075 × 10^{7}

Question 3.

On average, the Moon’s distance from Earth is about 384,400 km. What is this distance in scientific notation? __________________

Answer:

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 × 10^{9} _______________

Answer:

1.0395 x 10^{9} in the standard form is

10^{9} = 1,000,000,000

1.0395 x 1,000,000,000 = 1,039,500,000.

Question 5.

4 × 10^{2} _______________

Answer:

4 x 10² in the standard form is

10² = 100

4 x 100 = 400

Question 6.

The population of Indonesia was about 2.48216 × 10^{8} people in 2011. What is this number in standard notation? _______________

Answer:

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 _______________

Answer:

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 ____

Answer:

0.000701 Given

7.01 Place the decimal point

4 Count the number of places the decimal point is moved

7.01 × 10^{4} 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} ______________

Answer:

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} ______________

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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?

Answer:

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 × 10^{2}

(B) 9 × 10^{2}

(C) 90 × 10^{1}

(D) 9 × 10^{1}

Answer:

The number 90 in the scientific notation is 9 × 10^{1}

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 × 10^{5} passengers

(B) 7.867 × 10^{2} passengers

(C) 7.867 × 10^{8} passengers

(D) 7.867 × 10^{9} passengers

Answer:

(C) 7.867 × 10^{8} 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.

10^{8} Write the answer as power of 10.

7.867 × 10^{8} Write the product of the results from above

There are 7.867 × 10^{8} passengers

Question 3.

In 2011, the population of Mali was about 1.584 × 10^{7} 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

Answer:

(C) 15,840,000 people

Explanation:

1.584 × 10^{7} 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

Answer:

(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

Answer:

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

Answer:

(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

Answer:

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

Answer:

(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.

Answer:

2.38 x 10^{-1} in the standard form is

10^{-1} = 0.1

2.38 x 0.1 = 0.238

Multiplying the 2.38 with 0.1 then you get 0.238.