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 × 103
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 × 103
c. 27.3 = ____
Answer: 2.73 × 101
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 × 101
Question 2.
a. 810.4 = ____
Answer: 8.104 × 102
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 × 102
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 × 102
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 × 102
c. 36,054 = ____
Answer: 3.6054 × 104
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 × 104
Question 4.
a. 50,210 = ____
Answer: 5.0210 × 104
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 × 104
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 × 102
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 × 102
Question 5.
a. 36.25 = ____
Answer: 3.625 × 101
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 × 101
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 × 103
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 × 103
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 × 105 = ____
Answer: 846000
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 5 times
8.46 × 105 = 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 × 104 = ____
Answer: 90200
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 4 times
9.02 × 104 = 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 × 103 = ____
Answer: 8450
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 3 times
8.45 × 103 = 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 × 103 = ____
Answer: 1060
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 3 times
1.06 × 103 = 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 × 104 = ____
Answer: 30200
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 4 times
3.02 × 104 = 30200
c. 1.56 × 104 = ____
Answer: 15600
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 4 times
1.56 × 104 = 15600
Write each number in scientific notation.
Question 1.
a. 32.5 = _____
Answer: 3.25 × 101
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 × 101
b. 6,708 = ____
Answer: 6.708 × 103
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 × 103
c. 387 = _____
Answer: 3.87 × 102
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 × 102
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 × 104
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 × 104
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 × 103
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 × 103
Question 4.
a. 98.25 = ____
Answer: 9.825 × 101
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 × 101
b. 2,385 = ___
Answer: 2.385 × 103
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 × 103
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 × 103
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 × 103
b. 418 = ____
Answer: 4.18 × 102
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 × 102
c. 75.183 = ____
Answer: 7.5183 × 101
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 × 101
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 × 103
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 × 103
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 × 103
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 × 103
b. 23.65 = ____
Answer: 2.365× 101
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× 101
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× 102
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× 102
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 × 105 = ____
Answer: 913000
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 5 times
9.13 × 105 = 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 × 104 = ____
Answer: 24300
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 4 times
2.43 × 104 = 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 × 103 = ____
Answer: 8480
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 3 times
8.48 × 103 = 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 × 103 = ____
Answer: 9470
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 3 times
9.47 × 103 = 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 × 104 = ____
Answer: 41300
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 4 times
4.13 × 104 = 41300
c. 3.78 × 104 = ____
Answer: 37800
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 4 times
3.78 × 104 = 37800
Question 13.
a. 3.12 × 103 = ____
Answer: 3120
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 3 times
3.12 × 103 = 3120
b. 1.329 × 105 = ____
Answer: 132900
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 5 times
1.329 × 105 = 132900
c. 8.69 × 102 = _____
Answer: 869
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 2 times
8.69 × 102 = 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 × 105 = ____
Answer: 356000
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 5 times
3.56 × 105 = 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 × 103 = ____
Answer: 2700
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 3 times
2.7 × 103 = 2700
Question 16.
a. 7.3 × 102 = ____
Answer: 730
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 2 times
7.3 × 102 = 730
b. 1.25 × 104 = ____
Answer: 12500
Translate numbers written in scientific notation into standard form by reading the exponent.
Move the decimal right 4 times
1.25 × 104 = 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