# Mathematics Grade 8 Practice Questions

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1. Convert 0.2 ? into a fraction.
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a. ^{1}/_{5}

b. ^{11}/_{50}

c. ^{2}/_{9}

d. ^{2}/_{7}

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2. What is the decimal expansion of ^{5}/_{6}?
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a. 0.(56)

b. 0.83

c. 0.56

d. 1.2

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3. Which number is the closest approximation to ^{π}/_{4}?
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a. 0.85

b. 1.0

c. 0.785

d. 1.273

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4. Without using a calculator, identify which point on the number line could be √3?.
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a. Point A

b. Point B

c. Point C

d. Point D

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5. Simplify 5 ^{2}x5^{4}x5^{-4}x5^{-2}.
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a. 1

b. 5

c. 0

d. 2.5

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6. Simplify ( ^{2}/_{3})^{-3}.
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a. ^{8}/_{27}

b. ^{27}/_{8}

c. ^{-8}/_{27}

d. ^{-27}/_{8}

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7. Solve the equation for x: x ^{2}=16
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a. x=4

b. x=±4

c. x=8

d. x=±8

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8. Solve the equation for x: x ^{3}=-27
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a. x=-9

b. x=±9

c. x=-3

d. x=±3

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9. What is the decimal notation of 7x10 ^{-4}?
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a. 70,000

b. 7,000

c. 0.00007

d. 0.0007

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10. What is 0.0143 written in scientific notation?
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a. 1.43x10

b. 1.43x10^{2}

c. 1.43x10^{-1}

d. 1.43x10^{-2}

## Answers and Explanations

1. C: When converting a decimal whose value repeats itself indefinitely, write the repeating digit or digits in the numerator. In this problem, the repeating digit is 2. In the denominator, place 9 for every repeating digit, then reduce the fraction to lowest terms. In this problem a single 9 is in the denominator, so the answer is ^{2}/_{9}. Another example is 0.‾24= ^{24}/_{99}=^{8}/_{33}

2. B: 5/6 can be rewritten as 5x6=0.83 ?

3. C: You can approximate ?=3.14. Then 3.14x4=0.785

4. C: See that 2^{2} =4 . Since 2^{2} > 3, we know √2^{2} > √3 which is to say √3 < 2. Similarly, see that √3 > 1. This means that √3 is between 1 and 2. The only point between those on the number line is point C.

5. A: When multiplying powers that have the same base, the exponents are added up, and the base remains the same. Here it would be: 5^{2}+4+(-4)+(-2) )=5^{0}. Then, using the zero exponent rule of a^{0}=1 whenever a ≠ 0, we find that the answer is 5^{0}=1

6. B: The negative exponent will take the reciprocal of the base, then the exponent will distribute to both the numerator and denominator and the powers will be simplified.
(2/3)^{-3}=(3/2)^{3}=3^{3}/2_{3} =27/8

7. B: When solving an equation of the form x^{n} =b, take the n^{th} root of both sides of the equation. If n is even, then it will need to be =±? ^{n}√ b , meaning there are two solutions, one positive and one negative. If n is even and b is less than zero, then no real solution exists.

x^{2}=16

√(x^{2} )=± √16

x=±4

8. C: When solving an equation of the form x^{n}=b, take the n^{th} root of both sides of the equation. If n is even, then it will need to be ±?^{n}√b, and if *n* is odd, it is only the ^{n}√ b. If *n* is odd, then there is only one solution and the sign of the answer is the sign of b.

x^{3}=-27

√ x^{3} = ^{3} √-27

x=-3

9. D: Because the exponent of 10 is -4, the decimal which is located behind the 7 will move 4 spaces to the left, and any of the empty spaces will fill with 0's. so 7x 10? ^{-4}=0.0007

10. D: 1.43x10^{-2} is the same as 1.43x^{1}/_{100} or .0143. To write a number in scientific notation, the form is ax10^{n}, where 1 ≤ a < 10. The decimal needs to move two spaces to the right so that it is immediately to the right of the 1. To move the decimal 2 places, we multiply by 100, but we also need to multiply by 10^{-2} to cancel. .0143=.0143x^{100}/_{100}=1.43x^{1}/_{100}=1.43 x?10^{-2}.

Last Updated: 04/18/2018