**1. Convert 0.2 ? into a fraction.**

^{1}/_{5}^{11}/_{50}^{2}/_{9}^{2}/_{7}

**2. What is the decimal expansion of **^{5}/_{6}?

^{5}/

_{6}?

- 0.(56)
- 0.83
- 0.56
- 1.2

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

^{π}/

_{4}?

- 0.85
- 1.0
- 0.785
- 1.273

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

- Point A
- b. Point B
- Point C
- Point D

**5. Simplify 5**^{2}x5^{4}x5^{-4}x5^{-2}.

^{2}x5

^{4}x5

^{-4}x5

^{-2}.

- 1
- 5
- 0
- 2.5

**6. Simplify (**^{2}/_{3})^{-3}.

^{2}/

_{3})

^{-3}.

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

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

^{2}=16

- x=4
- x=±4
- x=8
- x=±8

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

^{3}=-27

- x=-9
- x=±9
- x=-3
- x=±3

**9. What is the decimal notation of 7×10**^{-4}?

^{-4}?

- 70,000
- 7,000
- 0.00007
- 0.0007

**10. What is 0.0143 written in scientific notation?**

- 1.43×10
- 1.43×10
^{2} - 1.43×10
^{-1} - 1.43×10
^{-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 5×6=0.83 ?

3. C: You can approximate ?=3.14. Then 3.14×4=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: 1.43×10^{-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}.

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by Enoch Morrison | Last Updated: January 9, 2019