Chapter 1 Test Study Guide

-64 You need to multiply (-4) x (-4) x (-4)

2. What is the value of the expression (−4)^3? TB pg 16

0.54545454... To change a fraction to a decimal, divide the numerator by the denominator using BLT or on a calculator.

1. What is the fraction 6/11 written as a decimal? TB pg 8, NB pg 20

2^-3 Remove the numerator. The base stays the same. The exponent becomes negative.

10. How is the fraction 1/2^3 written using a negative exponent? TB pg 44, NB pg 24

0.00003471 Start at the decimal. The exponent tells you to jump five jumps to the left (negative = jump to the left). Fill in the empty jumps with zeros and CROSS OUT the old decimal.

11. What is 3.471 × 10^-5 written in standard form? TB pg 52, NB pg 26

8.64 X 10^4 The new decimal goes between the 8 and 6. Jump from NEW TO OLD (4 jumps to the right). Write the new number 8.64. The base stays 10. The exponent is 4 (4 jumps to the right, right = positive exponent).

12. In one 24-hour day there are 86,400 seconds. What is this number written in scientific notation? TB pg 52, NB pg 27

7.5 x 10^5 Regroup the number parts together and the powers together. Multiply the number parts (2.5*3). Keep the base the same. Use the shortcut to add the exponents (3 + 2)

13. What is the value of the expression below written in scientific notation? (2.5 × 10^3)(3 × 10^2) TB pg 60, NB pg 28

1.9 x 10^3 Since the exponent is the same, subtract the number parts (4.7 - 2.8) and keep the power the same.

14. What is the value of the expression below written in scientific notation? (4.7 × 10^3) - (2.8 × 10^3) TB pg 61, NB pg 30

8.823 x 10^5 Write as a division problem (as a fraction). 3 × 10^8/3.4 × 10^2. Divide the number parts (3 / 3.4 = 0.8823). Use the shortcut: keep the base the same and subtract the exponents (8-2=6) 0.8823 x 10^6 --------> 0.8823 is not between 1 and 10. 8.823 x 10^-1 x 10^6 --------> move the decimal one jump to the left, and write the power, the drop down the 10^6. Add the exponents, keep the base the same to get one power. 8.823 x 10^5

15. The speed of light is approximately 3 × 10^8 meters per second, while the speed of sound is approximately 3.4 × 10^2 meters per second. How many times faster is the speed of light than the speed of sound? TB pg 60, NB pg 29

y = 8 Square root both sides of the equation. √y^2 = √64 y = 8

16. What is the solution of the equation y^2 = 64? TB pg 72, NB pg 32

approximately 5 √29 is between √25 and √36. It is closer to √25, therefore the √29 is approximately 5

17. Estimate √29. Do not use a calculator. TB pg 82, NB pg 34

rational Any number that can be written as a fraction is a rational number. Fractions, decimals -terminating and repeating, percents, mixed numbers, and square roots of perfect squares are all rational

18. Is 7/8 rational or irrational? TB pg 90, NB pg 36

2 1/3, √6, √7, 9/3 Change all to decimals then compare. Write the original numbers when writing in order. √7 = 2.64 2 1/3 = 2.33 9/3 = 3 √6 = 2.44

19. Write the following numbers in ordered from least to greatest? √7 2 1/3 9/3 √6 TB pg 91

2 ∛8 means you need to find the number to the third power that will equal 8. _____ x ______ x _______ = 8 __2___ x ___2___ x ___2____ = 8

20. What is the value of ∛8? TB pg 73, NB pg 33

7/9 y = 0.777... x10 x10 10y = 7.777... -1y -0.777... 9y = 7 /9 /9 (Divide both sides by 9) y =7/9

3. Convert 0.777.... to a fraction in simplest form? TB pg 9, NB pg 22

10 ^12 When dividing powers with the same base, the shortcut is to subtract the exponents and the base stays the same.

4. Using exponents, what is the simplified form of the expression 10^15 / 10^3 ? TB pg 25, NB pg 24

6 ^7 When multiplying powers with the same base, the shortcut is to add the exponents and keep the base the same.

5. Using exponents, what is the simplified form of the expression 6^5 • 6^2? TB pg 24, NB pg 24

5^4 To find the area of a square shape, multiply length times width or square the sides. If the side of Rachel's garden is 5^2 you need to solve (5^2)^2. Use the power of a power rule and multiply the exponents. The base stays the same.

6. Rachel's garden is square in shape. The length of one side of her garden is 5^2 feet. What is the area of her garden in square feet? Express your answer using exponents. TB pg 32, NB pg 24

3^3 x^12 Write the invisible exponent (1) on the 3, then use the Power of a Power rule and multiply the exponents. The bases stay the same. Write the 3, multiply the exponents 1x3. Write the x and multiply the exponents 4x3.

7. What is the simplified form of the expression (3x^4)^3? TB pg 33, NB pg 24

x^12 The base stays the same. Multiply the exponents.

8. Simplify (x^4)^3 TB pg 32, NB pg 24

1/5^3 Write it as a fraction. The numerator is 1. The base stays the same. The exponent changes to positive.

9. How is the expression 5^−3 written using a positive exponent? TB pg 44, NB pg 24