ReviewUnit1:Exponents
No calculator necessary. Please do not use a calculator.
Unit 1 Goals
• Know and apply the properties of integer exponents to generate equivalent numerical expressions. (8.EE.1)
• Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very
small quantities, and to express how many times as much one is than the other. (8.EE.3)
• Perform operations with numbers expressed in scientific notation, including problems where both decimal and
scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of
very large or very small quantities. Interpret scientific notation that has been generated by technology.
(8.EE.4)
Evaluate, meaning multiply out the exponent, giving your answer as a fraction when necessary.
1. 4 × 4
5. ( )
1
6.
4
3. (6 )
16
9.
2. (3 )(3 )
×!
7. ( )( )
8. (5 )
125
10. (# ) × # "
4. 11.
($! )"
1
$"
16
$%
Determine if the following equations are true. Justify your answer.
( %
(
*
13. 8 × 8 = 8 × 8
14. (# ) =
True, 8 = 8
False, # ≠ #
15.
$! ×$"
$
False, +
$
= $%
≠ +
16. (4 ) = (4 )
True, 4 = 4
Determine the appropriate exponent to make the equation true.
17.
5
,"
,"
0%
= (- ) ?
19. 01 =
7
18. 2 × 2 = 2 × 2 ?
−4
0
0?
20.
5
23 4
3
= 59 ? 7
12.
× 4
Write the following numbers in scientific notation.
21. 9,089,000,000
9.089 × 103
22. 810,000,000,000
8.1 × 10
23. 0.00000027
2.7 × 10
24. 0.00106
1.06 × 10
27. 3.1 × 10
0.00000031
28. 7.109 × 10
71,090
Write the following numbers in standard form.
25. 5.14 × 10
0.00000514
26. 4.07 × 103
4,070,000,000
Choose the best unit of measurement for the following problems.
29. Would the weight of a strand of hair, about 6.9 × 10 grams, be best expressed using tons, pounds, or
milligrams?
Milligrams
30. Would the area of the City of Charleston, about 24.9 × 10 square centimeters, be best expressed using
square kilometers, square meters, or square millimeters?
Square kilometers
Estimate each of the following as a single digit times a power of ten. Then compute each of the following giving
your answer in scientific notation.
31. (2.1 × 10 )(500)
≈ 1 × 103
1.05 × 103
.×1
32. ×!
≈ 2 × 10
2.1 × 10
.*×!
33. 4.2 × 10 − 3,000,000
≈ 4 × 10
3.9 × 10
34. 6.2 × 10 + 0.000005
35.
36. (3 × 103 )(2,300)
×
≈ 1 × 10
≈ 1 × 10
≈ 6 × 10
1.12 × 10
1.2 × 10
6.9 × 10
Answer the following questions giving both an estimated answer (single digit times a power of ten) and a
precise answer (scientific notation).
37. In the United States, there are approximately 300,000,000 people that use a total of approximately
360,000,000,000 gallons of water in a day. How much water does each person use?
≈ 1 × 10
1.2 × 10
38. A football field has an area of 56,560>? and a tennis court 2,800>? . How many times bigger in area is a
football field than a tennis court?
≈ 2 × 10
2.02 × 10
39. Three thousand people sued McDonald’s for hot coffee and were compensated at least $280,000 for each
person. How much money was distributed in total?
≈ 9 × 10*
8.4 × 10*
40. There were 9,700,000 Macintosh computers sold in 2008. If Macintosh earns an average of $200 profit per
computer sold, how much profit did the company make selling computers in 2008?
≈ 2 × 103
1.94 × 103