Students can use the **Spectrum Math Grade 8 Answer Key** **Chapter 1 Lesson 1.4 Scientific Notation** as a quick guide to resolve any of their doubts.

## Spectrum Math Grade 8 Chapter 1 Lesson 1.4 Scientific Notation Answers Key

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10. Any number can be expressed in scientific notation.

Translate numbers written in scientific notation into standard form by reading the exponent.

**Write each number in scientific notation.**

Question 1.

a. 0.013 = ____

Answer: 1.3 × 10^{-2}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 2 places and multiply the shift by the power of 10.

0.013 = 1.3 × 10^{-2}

b. 4105 = _____

Answer: 4.105 × 10^{3}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 3 places and multiply the shift by the power of 10.

4105 = 4.105 × 10^{3}

c. 27.3 = ____

Answer: 2.73 × 10^{1}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 1 places and multiply the shift by the power of 10.

27.3 = 2.73 × 10^{1}

Question 2.

a. 810.4 = ____

Answer: 8.104 × 10^{2}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 2 places and multiply the shift by the power of 10.

810.4 = 8.104 × 10^{2}

b. 0.684 = ____

Answer: 6.84 × 10^{-1}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 1 places and multiply the shift by the power of 10.

0.684 = 6.84 × 10^{-1}

c. 0.017 = _____

Answer: 1.7 × 10^{-2}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 2 places and multiply the shift by the power of 10.

0.017 = 1.7 × 10^{-2}

Question 3.

a. 0.0006 = ____

Answer: 6 × 10^{-4}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 4 places and multiply the shift by the power of 10.

0.0006 = 6 × 10^{-4}

b. 427.5 = ___

Answer: 4.275 × 10^{2}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 2 places and multiply the shift by the power of 10.

427.5 = 4.275 × 10^{2}

c. 36,054 = ____

Answer: 3.6054 × 10^{4}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 4 places and multiply the shift by the power of 10.

36,054 = 3.6054 × 10^{4}

Question 4.

a. 50,210 = ____

Answer: 5.0210 × 10^{4}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 4 places and multiply the shift by the power of 10.

50,210 = 5.0210 × 10^{4}

b. 0.0005 = ____

Answer: 5 × 10^{-4}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 4 places and multiply the shift by the power of 10.

0.0005 = 5 × 10^{-4}

c. 256.21 = ____

Answer: 2.5621 × 10^{2}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 2 places and multiply the shift by the power of 10.

256.21 = 2.5621 × 10^{2}

Question 5.

a. 36.25 = ____

Answer: 3.625 × 10^{1}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 1 places and multiply the shift by the power of 10.

36.25 = 3.625 × 10^{1}

b. 0.892 = ____

Answer: 8.92 × 10^{-1}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 1 places and multiply the shift by the power of 10.

0.892 = 8.92 × 10^{-1}

c. 0.00065 = _____

Answer: 6.5 × 10^{-4}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 4 places and multiply the shift by the power of 10.

0.00065 = 6.5 × 10^{-4}

Question 6.

a. 0.027 = ____

Answer: 2.7 × 10^{-2}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 2 places and multiply the shift by the power of 10.

0.027 = 2.7 × 10^{-2}

b. 1,416.3 = ____

Answer: 1.4163 × 10^{3}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 1 places and multiply the shift by the power of 10.

1,416.3 = 1.4163 × 10^{3}

c. 0.0049 = _____

Answer: 4.9 × 10^{-3}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 3 places and multiply the shift by the power of 10.

0.0049 = 4.9 × 10^{-3}

**Write each number in standard form.**

Question 7.

a. 2.6 × 10^{-3} = ____

Answer: 0.0026

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 3 times

2.6 × 10^{-3} = 0.0026

b. 8.46 × 10^{5} = ____

Answer: 846000

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 5 times

8.46 × 10^{5} = 846000

c. 4.65 × 10^{-1} = ____

Answer: 0.465

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 1 time

4.65 × 10^{-1} = 0.465

Question 8.

a. 9.02 × 10^{4} = ____

Answer: 90200

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 4 times

9.02 × 10^{4} = 90200

b. 5.15 × 10^{-2} = ____

Answer:

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 1 time

c. 8.45 × 10^{3} = ____

Answer: 8450

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 3 times

8.45 × 10^{3} = 8450

Question 9.

a. 7.25 × 10^{-4} = ____

Answer: 0.000725

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 4 time

7.25 × 10^{-4} = 0.000725

b. 1.06 × 10^{3} = ____

Answer: 1060

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 3 times

1.06 × 10^{3} = 1060

c. 9.06 × 10^{-5} = ____

Answer: 0.0000906

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 5 time

9.06 × 10^{-5} = 0.0000906

Question 10.

a. 9.7 × 10^{-3} = ____

Answer: 0.0097

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 3 time

9.7 × 10^{-3} = 0.0097

b. 3.02 × 10^{4} = ____

Answer: 30200

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 4 times

3.02 × 10^{4} = 30200

c. 1.56 × 10^{4} = ____

Answer: 15600

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 4 times

1.56 × 10^{4} = 15600

**Write each number in scientific notation.**

Question 1.

a. 32.5 = _____

Answer: 3.25 × 10^{1}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 1 places and multiply the shift by the power of 10.

32.5= 3.25 × 10^{1}

b. 6,708 = ____

Answer: 6.708 × 10^{3}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 3 places and multiply the shift by the power of 10.

6708= 6.708 × 10^{3}

c. 387 = _____

Answer: 3.87 × 10^{2}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 2 places and multiply the shift by the power of 10.

387= 3.87 × 10^{2}

Question 2.

a. 0.569 = ____

Answer: 5.69 × 10^{-1}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 1 places and multiply the shift by the power of 10.

0.569 = 5.69 × 10^{-1}

b. 67,345 = ____

Answer: 6.7345 × 10^{4}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 4 places and multiply the shift by the power of 10.

67,345 = 6.7345 × 10^{4}

c. 0.027 = ____

Answer: 2.7 × 10^{-2}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 2 places and multiply the shift by the power of 10.

0.027 = 2.7 × 10^{-2}

Question 3.

a. 0.079 = ____

Answer: 7.9 × 10^{-2}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 2 places and multiply the shift by the power of 10.

0.079 = 7.9 × 10^{-2}

b. 0.51 = ____

Answer: 5.1 × 10^{-1}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 1 places and multiply the shift by the power of 10.

0.51 = 5.1 × 10^{-1}

c. 6,791 = _____

Answer: 6.791 × 10^{3}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 3 places and multiply the shift by the power of 10.

6,791 = 6.791 × 10^{3}

Question 4.

a. 98.25 = ____

Answer: 9.825 × 10^{1}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 1 places and multiply the shift by the power of 10.

98.25 = 9.825 × 10^{1}

b. 2,385 = ___

Answer: 2.385 × 10^{3}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 3 places and multiply the shift by the power of 10.

2,385 = 2.385 × 10^{3}

c. 0.413 = ____

Answer: 4.13 × 10^{-4}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 4 places and multiply the shift by the power of 10.

0.413 = 4.13 × 10^{-4}

Question 5.

a. 7,831 = ____

Answer; 7.831 × 10^{3}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 3 places and multiply the shift by the power of 10.

7,831 = 7.831 × 10^{3}

b. 418 = ____

Answer: 4.18 × 10^{2}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 2 places and multiply the shift by the power of 10.

418= 4.18 × 10^{2}

c. 75.183 = ____

Answer: 7.5183 × 10^{1}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 1 places and multiply the shift by the power of 10.

75.183 = 7.5183 × 10^{1}

Question 6.

a. 0.0004 = ____

Answer: 4 × 10^{-4}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 4 places and multiply the shift by the power of 10.

0.0004= 4 × 10^{-4}

b. 7,301.4 = ____

Answer: 7.3014 × 10^{3}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 3 places and multiply the shift by the power of 10.

7,301.4 = 7.3014 × 10^{3}

c. 0.0018 = ____

Answer: 1.8 × 10^{-3}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 3 places and multiply the shift by the power of 10.

0.0018= 1.8 × 10^{-3}

Question 7.

a. 5,624 = ____

Answer: 5.624 × 10^{3}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 3 places and multiply the shift by the power of 10.

5,624 = 5.624 × 10^{3}

b. 23.65 = ____

Answer: 2.365× 10^{1}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 1 places and multiply the shift by the power of 10.

23.65 = 2.365× 10^{1}

c. 0.965 = ____

Answer: 9.65 × 10^{-1}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 1 places and multiply the shift by the power of 10.

0.965 = 9.65 × 10^{-1}

Question 8.

a. 0.0045 = ____

Answer: 4.5 × 10^{-3}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 3 places and multiply the shift by the power of 10.

0.0045 = 4.5 × 10^{-3}

b. 523 = ____

Answer: 5.23× 10^{2}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal left 2 places and multiply the shift by the power of 10.

523 = 5.23× 10^{2}

c. 0.355 = ____

Answer: 3.55 × 10^{-1}

Scientific notation is most often used as a concise way of writing very large and very small numbers. It is written as a number between 1 and 10 multiplied by a power of 10.

Move the decimal right 1 places and multiply the shift by the power of 10.

0.355 = 3.55 × 10^{-1}

**Write each number in standard form.**

Question 9.

a. 9.13 × 10^{5} = ____

Answer: 913000

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 5 times

9.13 × 10^{5} = 913000

b. 4.02 × 10^{-3} = ____

Answer: 0.00402

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 3 times

4.02 × 10^{-3} = 0.00402

c. 2.43 × 10^{4} = ____

Answer: 24300

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 4 times

2.43 × 10^{4} = 24300

Question 10.

a. 1.124 × 10^{-1} = _____

Answer: 0.1124

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 1 time

1.124 × 10^{-1} = 0.1124

b. 8.48 × 10^{3} = ____

Answer: 8480

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 3 times

8.48 × 10^{3} = 8480

c. 5.12 × 10^{-2} = ____

Answer: 0.0512

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 2 times

5.12 × 10^{-2} = 0.0512

Question 11.

a. 9.47 × 10^{3} = ____

Answer: 9470

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 3 times

9.47 × 10^{3} = 9470

b. 3.28 × 10^{-4} = ____

Answer: 0.000328

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 4 times

3.28 × 10^{-4} = 0.000328

c. 6.73 × 10^{-3} = ____

Answer: 0.00673

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 3 times

6.73 × 10^{-3} = 0.00673

Question 12.

a. 5.3 × 10^{-5} = ____

Answer: 0.000053

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 5 times

5.3 × 10^{-5} = 0.000053

b. 4.13 × 10^{4} = ____

Answer: 41300

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 4 times

4.13 × 10^{4} = 41300

c. 3.78 × 10^{4} = ____

Answer: 37800

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 4 times

3.78 × 10^{4} = 37800

Question 13.

a. 3.12 × 10^{3} = ____

Answer: 3120

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 3 times

3.12 × 10^{3} = 3120

b. 1.329 × 10^{5} = ____

Answer: 132900

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 5 times

1.329 × 10^{5} = 132900

c. 8.69 × 10^{2} = _____

Answer: 869

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 2 times

8.69 × 10^{2} = 869

Question 14.

a. 4.5 × 10^{-4} = ____

Answer: 0.00045

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 4 times

4.5 × 10^{-4} = 0.00045

b. 9.8 × 10^{-6} = ____

Answer: 0.0000098

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 6 times

9.8 × 10^{-6} = 0.0000098

c. 3.56 × 10^{5} = ____

Answer: 356000

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 5 times

3.56 × 10^{5} = 356000

Question 15.

a. 5.42 × 10^{-2} = ____

Answer: 0.0542

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 2 times

5.42 × 10^{-2} = 0.0542

b. 9.08 × 10^{-8} = ____

Answer: 0.0000000908

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 8 times

9.08 × 10^{-8} = 0.0000000908

c. 2.7 × 10^{3} = ____

Answer: 2700

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 3 times

2.7 × 10^{3} = 2700

Question 16.

a. 7.3 × 10^{2} = ____

Answer: 730

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 2 times

7.3 × 10^{2} = 730

b. 1.25 × 10^{4} = ____

Answer: 12500

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal right 4 times

1.25 × 10^{4} = 12500

c. 8.8 × 10^{-8} = ____

Answer: 0.000000088

Translate numbers written in scientific notation into standard form by reading the exponent.

Move the decimal left 8 times

8.8 × 10^{-8} = 0.000000088