Free Printable OUR Unit 7 Review

1.

10^4\cdot10^3

Mark the equivalent expressions:

a)

$10^7$

b)

$10^{4+3}$

c)

$10^{12}$

d)

$10^{4\cdot3}$

2.

In order to multiply powers with the same base, we add their exponents.

a)

True

b)

False

3.

$10^5\cdot10^3$

Simplify to an equivalent expression.

a)

$10^8$

b)

1,000,000,000,000,000

c)

$10^{15}$

d)

10,000,000

4.

Which expressions are equivalent to

10^5

a)

$10\cdot10\cdot10\cdot10\cdot10$

b)

$10^1\cdot10^5$

c)

$100,000$

d)

$10^3+10^2$

5.

$10^{96}$ is (a) times bigger than $10^{94}$

6.

How would you write 5.6 x 10^-3 in standard form?

a)

56,000

b)

5,600

c)

0.00056

d)

0.0056

7.

Scientific notation is made up of two number parts:

$a\times10^n$

$a$ should be number between 1 and 100.

a)

True

b)

False

8.

How would you write 0.0005 in scientific notation?

a)

50 x 10⁵

b)

5 x 10⁴

c)

5 x 10³

d)

.5 x 10³

9.

Which of these numbers are NOT in scientific notation?

a)

1.2 x 10³

b)

5.3 x 10⁹

c)

2.0 x 10⁰

d)

10 x 10²

10.

Give the sum of (2.6 x 10⁶) + (4.2 x 10⁶)

a)

6.8 x 10⁶

b)

6.8 x 10¹²

c)

8.4 x 10⁶

d)

3.2 x 10¹²

11.

Give the sum of (8.7 x 10⁵) + (7.32 x 10⁷) in scientific notation

a)

16.02 x 10⁷

b)

7.407 x 10⁵

c)

7.407 x 10⁷

d)

1.602 x 10⁷

12.

Give the difference of (6.4 x 10^-6) - (5.7 x 10^-7)

a)

5.83 x 10^-6

b)

7 x 10^-7

c)

1.23 x 10^-13

d)

1.3 x 10^-6

13.

Give the sum of (5.7 x 10^-7) + (3.23 x 10^-5)

a)

1.193 x 10^-12

b)

3.287 x 10^-5

c)

3.317 x 10^-12

d)

5.53 x 10^-2

14.

The mega in megabyte means

a)

1,000

b)

1,000,000

c)

1,000,000,000

d)

1,000,000,000,000

15.

The kilo in kilobyte means

a)

1,000

b)

1,000,000

c)

1,000,000,000

d)

1,000,000,000,000

16.

The tera in terabyte means

a)

1,000

b)

1,000,000

c)

1,000,000,000

d)

1,000,000,000,000

17.

The giga in gigabyte means

a)

1,000

b)

1,000,000

c)

1,000,000,000

d)

1,000,000,000,000

18.

Select all the expressions that are equivalent to

6^{-4}

a)

-24

b)

$3^{-8}$

c)

$\frac{1}{6^4}$

d)

$\left(\frac{1}{6}\right)\cdot\left(\frac{1}{6}\right)\cdot\left(\frac{1}{6}\right)\cdot\left(\frac{1}{6}\right)$

e)

24

19.

Which of the following is the expression in a single exponent?

\frac{5^4}{5^8}

a)

$5^4$

b)

$5^{-4}$

c)

$5^{\frac{1}{2}}$

d)

$5^2$

20.

Which of the following is the expression in a single exponent?

\left(14^4\right)^2

a)

$14^6$

b)

$14^2$

c)

$14^8$

d)

$14^{\frac{1}{2}}$

21.

Which of the following is the expression in a single exponent?

\left(12^3\right)^{-5}

a)

$12^{-2}$

b)

$12^{-15}$

c)

$12^{15}$

d)

$-12^{15}$

22.

Which of the following is the expression in a single exponent?

7^3\cdot7^5

a)

$7^8$

b)

$7^{15}$

c)

$7^{-2}$

d)

$\frac{1}{7^2}$

23.

Which of the following is the expression in a single exponent?

7^3+7^5

a)

$7^8$

b)

$7^{15}$

c)

$7^{-2}$

d)

None of the above

24.

What is the value of

10^0

a)

0

b)

10

c)

1

d)

Undefined

25.

What is the rule for dividing powers of ten?

a)

$\frac{10^n}{10^m}=10^{\frac{n}{m}}$

b)

$\frac{10^n}{10^m}=10^{n-m}$

c)

$\frac{10^n}{10^m}=10^n-10^m$

d)

$\frac{10^n}{10^m}=n-m$

26.

Which expressions have the same value as

10^7

a)

$\frac{10^{10}}{10^3}$

b)

$10^3+10^4$

c)

$10^0\cdot10^6\cdot10$

d)

$\frac{10^{14}}{2}$

e)

$\left(10^3\right)^4$

27.

Evaluate:

10^3+10^2+10^1+10^0

(a)

28.

Write the expression as a single power of 10:

\left(\frac{10^6}{10^2}\right)^3

a)

$10^9$

b)

$10^7$

c)

$10^8$

d)

$\left(10^4\right)^3$

e)

$10^{12}$

29.

Write the expression as a single power of 10: $\frac{\left(10^2\right)^6}{\left(10^3\right)^2}$

a)

$10^2$

b)

$10^4$

c)

$10^6$

d)

$10^3$

e)

$\frac{10^{10}}{10^6}$

30.

Is this equation true or false?

$5\times10^7\times5\times10^5=5\times10^{35}$

a)

True

b)

False

c)

Neither true nor false, it simply exists

d)

There is no way to determine

31.

Is this equation true or false?

$\frac{5\times10^7}{7\times10^5}=\left(5\div7\right)\times10^2$

a)

True

b)

False

c)

Neither true nor false, it simply exists

d)

There is no way to determine

32.

If there are $2.4\times10^8$ bacteria in a cup of yogurt and the mass of a single bacterium is $1\times10^{-12}$ grams, what is the mass of all the bacteria in the yogurt?

a)

$2.4\times10^{20}$ grams

b)

$2.4\times10^4$ grams

c)

$2.4\times10^{-20}$ grams

d)

$2.4\times10^{-4}$ grams

33.

Continents move at about $7.9\times10^{-8}$ centimeters per second. Estimate how long would it take to move one centimeter?

(There are about $3.15\times10^7$ seconds in a year)

a)

about 50 years

b)

about 5 years

c)

about 0.5 years

d)

about 0.05 years

34.

The diameter of the sun is $1.39\times10^6$ One of the the largest known stars, UY Scuti, has a diameter of $2.37\times10^9$

Estimate how many suns side-by-side would have the same width as UY Scuti.

a)

100

b)

1000

c)

200

d)

2000

35.

The nearest star is approximately 40 trillion kilometers away. Write this as a power of 10.

a)

$4^{12}$

b)

$4\cdot10^{12}$

c)

$40^{12}$

d)

$4\cdot10^{13}$

36.

There are about 70,000 drops of water in a gallon. An Olympic swimming pool takes about $6\cdot10^5$ gallons of water to fill. How many drops of water would it take to fill an Olympic swimming pool?

a)

42,000,000

b)

$42\cdot10^{10}$

c)

$4.2\cdot10^{10}$

d)

4,200,000,000

37.

There are about 37 trillion cells in a human body. There are about 10 million ribosomes in each cell. About how many ribosomes are there in a human body?

a)

$3.7\cdot10^{19}$

b)

$3.7\cdot10^{20}$

c)

$3.7\cdot10^{84}$

d)

$3.7\cdot10^{85}$

38.

About one million grains of sand fit in a cubic inch. A conic (cone shaped) pile of sand 3 inches high and a radius of 1 foot would have how many grains of sand?

a)

$48\pi\cdot10^6$

b)

$\pi\cdot10^6$

c)

$48\cdot10^6$

d)

$144\pi\cdot10^6$

39.

The moon is about $3.6\cdot10^8$ meters from earth. If a US dollar bill is 0.01 cm thick could a stack of a trillion one dollar bills reach the moon?

a)

Yes, a trillion is $10^{12}$ and $0.01\cdot10^{12}=10^{10}$ which is bigger than $3.6\cdot10^8$ .

b)

Yes, a centimeter is 1/100 of a meter. A trillion is $10^{12}$ and that is bigger than $3.6\cdot10^8$ .

c)

No, a trillion is $10^{12}$ and $0.01\cdot10^{12}=10^{10}$ cm $=10^8$ meters .

d)

No, $3.6\cdot10^4$ meters is $3.6\cdot10^4$ kilometers which is longer than centimeters.

40.

Evaluate the expression. Use scientific notation to express your answer:

$\left(1.5\times10^3\right)\left(4\times10^8\right)$

a)

$6\times10^{11}$

b)

$6\times10^{24}$

c)

$5.5\times10^{11}$

d)

$5.5\times10^{24}$

41.

Evaluate the expression. Use scientific notation to express your answer:

$\frac{2.5\times10^{-9}}{5\times10^{-2}}$

a)

$2\times10^{-11}$

b)

$2\times10^{-7}$

c)

$0.5\times10^{-7}$

d)

$5\times10^{-8}$

42.

Evaluate the expression. Use scientific notation to express your answer:

$\left(6\times10^3\right)\left(3\times10^8\right)$

a)

$18\times10^{11}$

b)

$18\times10^{24}$

c)

$1.8\times10^{11}$

d)

$1.8\times10^{12}$

43.

Evaluate the expression. Use scientific notation to express your answer:

$\left(4.8\times10^3\right)\div\left(1.2\times10^8\right)$

a)

$4\times10^{11}$

b)

$4\times10^{-5}$

c)

$0.4\times10^{11}$

d)

$0.4\times10^{-5}$

44.

Estimate how many times larger $7.2\times10^7$ is than $3.4\times10^{-3}$

a)

$\approx200\$ billion times larger

b)

$\approx20$ billion times larger

c)

2.322580645 times larger

d)

$\approx20,000$ times larger

45.

Which expressions are equivalent to

\left(10^3\right)^2

a)

$10^6$

b)

$10^5$

c)

$10^{3\cdot2}$

d)

$10^3\cdot10^3$

46.

What is

\left(10^2\right)^4

in expanded form?

a)

$\left(10\cdot10\right)\left(10\cdot10\right)\left(10\cdot10\right)\left(10\cdot10\right)$

b)

$\left(10\cdot10\right)\left(10\cdot10\right)$

c)

$\left(10\cdot10\right)+\left(10\cdot10\right)+\left(10\cdot10\right)+\left(10\cdot10\right)$

d)

$\left(10\cdot10\right)\left(10\cdot10\right)\left(10\cdot10\right)$

47.

What is the rule?

\left(10^n\right)^m=

?

a)

$10^{n+m}$

b)

$10^{n\cdot m}$

c)

$10^{n-m}$

d)

$10^{n\div m}$

48.

Which expressions are equivalent to

10^6

a)

$\left(10\cdot10\right)\left(10\cdot10\right)\left(10\cdot10\right)$

b)

$1,000,000$

c)

$\left(10^2\right)^3$

d)

$\left(10^2\cdot10^2\right)^2$

49.

What is the expression in a single exponent? $\left(10^2\right)^8$

a)

$\left(10^2\right)^8$

b)

$10^{16}$

c)

$10^{10}$

d)

$10^4$

50.

What is the value of

10^0

a)

0

b)

10

c)

1

d)

Undefined

51.

What is the rule for dividing powers of ten?

a)

$\frac{10^n}{10^m}=10^{\frac{n}{m}}$

b)

$\frac{10^n}{10^m}=10^{n-m}$

c)

$\frac{10^n}{10^m}=10^n-10^m$

d)

$\frac{10^n}{10^m}=n-m$

52.

Which expressions have the same value as

10^7

a)

$\frac{10^{10}}{10^3}$

b)

$10^3+10^4$

c)

$10^0\cdot10^6\cdot10$

d)

$\frac{10^{14}}{2}$

e)

$\left(10^3\right)^4$

53.

Evaluate:

10^3+10^2+10^1+10^0

(a)

54.

Write the expression as a single power of 10:

\left(\frac{10^6}{10^2}\right)^3

a)

$10^9$

b)

$10^7$

c)

$10^8$

d)

$\left(10^4\right)^3$

e)

$10^{12}$

55.

Write the expression as a single power of 10: $\frac{\left(10^2\right)^6}{\left(10^3\right)^2}$

a)

$10^2$

b)

$10^4$

c)

$10^6$

d)

$10^3$

e)

$\frac{10^{10}}{10^6}$

56.

Which expression has an exponent?

a)

$x!\cdot4=3!$

b)

$x^2=16$

c)

$4x=16$

d)

$12+x=16$

57.

What is equivalent to

2^3

?

a)

8

b)

6

c)

5

d)

16

58.

Are the following equalvalent?

x\cdot x\cdot x\cdot x=4x

a)

Yes; for example: four ones makes 4!

b)

No; $4x=x+x+x+x$ and $x\cdot x\cdot x\cdot x=x^4$

c)

It depends on the value of $x$ .

d)

No; $x\cdot x\cdot x\cdot x=x\cdot4$

59.

Select all the expression equivalent to

3\cdot3\cdot3\cdot3\cdot3\cdot3

a)

$3^6$

b)

$3^3\cdot3^3$

c)

729

d)

$6\cdot3$

60.

Compare

2^{14}

and

2^{19}

a)

$2^{19}$ is 32 times bigger than $2^{14}$

b)

$2^{19}$ is 5 times bigger than $2^{14}$

c)

$2^{19}$ is about 500,000 more than $2^{14}$

d)

$2^{19}$ is about 10 more than $2^{14}$

61.

What is the value of $4^2$ ?

(a)

62.

What is the exponent rule for negative exponents?

a)

$10^{-n}=\frac{1}{10^n}$

b)

$10^{-n}=10^n$

c)

$10^{-n}=\frac{1}{10^{-n}}$

d)

$10^{-n}=10^{\frac{1}{n}}$

63.

Which expressions are equal to

\frac{1}{10^3}

a)

$\frac{1}{1000}$

b)

$\frac{1}{100}$

c)

$10^{-3}$

d)

$\frac{10^6}{10^9}$

e)

0.001

64.

Which expression is equivalent to the following fraction:

\frac{1}{1,000,000,000}

a)

$\frac{1}{10^9}$

b)

$10^{-9}$

c)

$10^9$

d)

$-10^9$

65.

$10^{-2}=\frac{10^6}{10^x}$ What value of $x$ would make this equation true?

(a)

66.

$\frac{1}{10}=10^{-2}$

Is this true? Why or why not?

a)

Yes, because 10 is two digits.

b)

Yes, because if you put them in the calculator they are equal

c)

No, because the 10 in the denominator has an exponent of 1 not 2.

d)

No, because if you put them in the calculator they are not equal

67.

$a^n$

Which letter represents the base?

a)

$a$

b)

$n$

c)

Neither

d)

Both

68.

$a^n$
Which letter represents the exponent?

a)

$a$

b)

$n$

c)

Neither

d)

Both

69.

What is $2^4\cdot3^4$ expanded?

a)

$\left(2+2+2+2\right)\cdot\left(3+3+3+3\right)$

b)

$4\left(2\right)\cdot4\left(3\right)$

c)

$\left(2\cdot2\cdot2\cdot2\right)\cdot\left(3\cdot3\cdot3\cdot3\right)$

d)

$\left(2\cdot2\cdot2\cdot2\right)+\left(3\cdot3\cdot3\cdot3\right)$

70.

How can I write this expression in a single exponent?

$2^4\cdot5^4$

a)

$10^4$

b)

$10^8$

c)

$2^4\cdot5^4$

d)

This can't be simplified

71.

$6^3\cdot2^3=12^x$
What value of $x$ would make this equation true?

(a)

72.

What is the rule for multiplying exponents of different bases?

a)

$a^n\cdot b^n=ab^n$

b)

$a^n\cdot b^m=ab^{n+m}$

c)

$a^n\cdot b^m=ab^{n\cdot m}$

d)

You can't multiply exponents with different bases

73.

What is point B as a power of 10?

a)

2

b)

$10^8$

c)

$2\cdot10^8$

d)

$2\cdot10^9$

74.

What is point A as a power of 10?

a)

3

b)

$10^5$

c)

$5.3\cdot10^8$

d)

$5.3\cdot10^9$

75.

What is the value of point B

a)

2

b)

200,000,000

c)

2,000,000,000

d)

2,000,000

76.

What is the value of point A

a)

3

b)

530,000,000

c)

5,300,000

d)

5,300,000,000

77.

Which expression(s) are equivalent to 437,000?

a)

$437\cdot10^3$

b)

$4.37\cdot10^5$

c)

$437\cdot10^5$

d)

$43.7\cdot10^2$

78.

What is the value of point A?

(a)

79.

How do you read this number?

1,000,000,000,000

a)

one trillion

b)

one billion

c)

one million

d)

one thousand million

80.

How do you read this number?

1,000,000,000

a)

one trillion

b)

one billion

c)

one million

d)

one hundred million

81.

How do you read this number?

0.001

a)

one ten thousandth

b)

one tenth

c)

one hundredth

d)

one thousandth

82.

How do you read this number?

0.000001

a)

one trillionth

b)

one billionth

c)

one millionth

d)

one hundred thousandth

83.

$344,000,000=344\cdot10^x$
What value of $x$ makes this equation true?

(a)

84.

$344,000,000=3.44\cdot10^x$
What value of $x$ makes this equation true?

(a)

85.

$344,000,000=34.4\cdot10^x$
What value of $x$ makes this equation true?

(a)

86.

Select all the expressions equal to 420 billion.

a)

$4.2\cdot10^{11}$

b)

$42\cdot10^{10}$

c)

$420\cdot10^9$

d)

$42\cdot10^9$

87.

Which is larger?

a)

A

b)

B

c)

C

d)

D

88.

Compare
$3\cdot10^{-8}$ and $4\cdot10^{-9}$

a)

$3\cdot10^{-8}>4\cdot10^{-9}$

b)

$3\cdot10^{-8}=4\cdot10^{-9}$

c)

$3\cdot10^{-8}<4\cdot10^{-9}$

89.

To graph $4\cdot10^{-16}$ on the number line what power of 10 would be used on the right?

a)

$10^{-15}$

b)

$10^{-16}$

c)

$10^{-17}$

90.

To graph $3.2\cdot10^{-10}$ on the number line what power of 10 would be used on the right?

a)

$10^{-9}$

b)

$10^{-10}$

c)

$10^{-11}$

91.

To graph 0.00000000066 on the number line what power of 10 would be used on the right?

a)

$10^{-9}$

b)

$10^{-10}$

c)

$10^{-11}$

92.

To graph 0.000000000066 on the number line what power of 10 would be used on the right?

a)

$10^{-9}$

b)

$10^{-10}$

c)

$10^{-11}$

93.

What is this number in scientific notation?

15,800

a)

$1.58\times10^4$

b)

$15.8\times10^4$

c)

$15.8\times10^3$

d)

$158\times10^2$

94.

What is this number in scientific notation?

0.00042

a)

$4.2\times10^4$

b)

$4.2\times10^{-4}$

c)

$42\times10^{-3}$

d)

$0.42\times10^{-5}$

95.

What is this number in scientific notation?

780,000,000,000

a)

$7.8\times10^9$

b)

$7.8\times10^{10}$

c)

$7.8\times10^{11}$

d)

$7.8\times10^{12}$

96.

What is this number in scientific notation?

0.00000000008

a)

$8\times10^{11}$

b)

$8\times10^{-10}$

c)

$8\times10^{-11}$

d)

$8\times10^{-12}$

97.

What is this number in scientific notation?

0.00000000008

a)

$8\times10^{11}$

b)

$8\times10^{-10}$

c)

$8\times10^{-11}$

d)

$8\times10^{-12}$

98.

What is this number in scientific notation?

6.8

a)

$6.8\times10^1$

b)

$6.8\times10^2$

c)

$6.8\times10^0$

d)

$6.8\times10^{-1}$

99.

What is this number in scientific notation?

6,800,000,000

a)

$6.8\times10^9$

b)

$6.8\times10^{10}$

c)

$6.8\times10^8$

d)

$68\times10^8$

100.

When raising a base with an exponent to another power, you _____ the exponents. Ex:

\left(6^{-3}\right)^5

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

101.

$7^5\times7^6$

a)

$49^{11}$

b)

$7^{11}$

c)

$14^{11}$

d)

$7^{30}$

102.

$3^{-3}\ \times3^8$

a)

$3^5$

b)

$3^{-24}$

c)

$9^5$

d)

$9^{-24}$

103.

$2^{-4}\times2^{-3}$

a)

$2^{-7}$

b)

$4^{-7}$

c)

$2^{12}$

d)

$4^{12}$

104.

$3^5\ \div\ 3^{28}$

a)

$3^{-23}$

b)

$9^{-23}$

c)

$3^{33}$

d)

$9^{33}$

105.

$2^{-5}\ \ \div2^4$

a)

$2^{-9}$

b)

$4^{20}$

c)

$4^{-20}$

d)

$2^{-1}$

106.

$10^0$

a)

0

b)

1

c)

10

d)

-10

107.

\left(6^{-3}\right)^5

a)

$6^{-15}$

b)

$6^2$

c)

$6^{-8}$

d)

$30^{-3}$

OUR Unit 7 Review

Total questions: 107

Worksheet time: 1hrs 13mins

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