1.1 - 1.7 Review

1.1 Repeating Decimals as Fractions

0

What are the steps to convert a repeating decimal to a fractions?

1. Assign the decimal as the variable.

2. Multiply by 10 (or 100, 1000, etc)

3. Subtract the variable from one side and the repeating decimal from the other.

4. Divide to solve for the variable.

100

Write 0.1 (with the 1 repeating) as a decimal.

1/9

100

Write 0.12 (with the 12 repeating) as a decimal.

12/99 = 4/33

200

Write 1.2 (with the 2 repeating) as a fraction.

11/9 = 1 2/9

200

Write 0.44 (with the 44 repeating) as a fraction.

44/99 = 4/9

1.2 Rational or Irrational?

0

A rational number means that it can be written as a....

FRACTION (aka ratio)

100

Is it Rational? Explain why or why not.

-2/5

Yes. It is Rational. Fractions are rational numbers because they are written as fractions. Negatives are included.

100

Is it Rational? Explain why or why not.

square root 27

No. It is Irrational. A square root must be a PERFECT SQUARE to be rational or else it cannot be written as a fraction. Bonus Point: Provide two examples of perfect squares.

200

Is it Rational? Explain why or why not.

0.4 with the 4 repeating.

Yes. It is Rational. Repeating decimals can be written as fractions so they are rational.

200

Is it Rational? Explain why or why not.

0.3526826384937...

No. It is irrational. Only terminating decimals and repeating decimals are rational. non-terminating decimals cannot be written as fractions so they are not rational.

1.3 Comparing Real Numbers

0

How do we estimate square roots that ARE NOT PERFECT SQUARES?

We determine the perfect square above and below. Then, we estimate by trial and error until close enough. Our answer is an approximation.

100

Estimate the root.

 square root. 5

approx2.2

100

Estimate the root.

square root. 20

approx 4.4

200

Estimate the root.

3root      51

approx 3.7

200

Estimate the root.

3root. 25

approx 2.3

1.4 Evaluating Square & Cube Roots

0

Evaluate the below.

square root 36

+- 6

100

Evaluate the below.

3 root 125

5

100

Evaluate the below.

square root 121

+- 11

200

Evaluate the below.

3 root  -64

-4

200

Evaluate the below.

square root  -4

Does Not Exist. Why?

1.5 Equations with Roots

0

What the inverse operation of an exponent?

Finding the root. So the inverse of squared is square root. The inverse of cubed is cube root. 

100

Evaluate the below.

z^2 = 1

+- 1

100

Evaluate the below.

x³ = -64

-4

200

Evaluate the below.

g² = 36

+- 6

200

Evaluate the below.

m³ = 125

5 (Why is it not 

+-??)

1.6 & 1.7 Exponent Properties

0

1. What do we do with the exponents when multiplying the same base?

2. What is the answer when the exponent is 0?

3. What does a negative exponent mean?

1. We add the exponents when multiplying the same base.

2. The answer is always 1 when the exponent is 0.

3. A negative exponent creates the reciprocal or puts the number under 1/x.

100

c² x c⁵

c⁷

100

3^-3

1/3^3 = 1/27

200

r⁴ x r^-2

r^-8  which is equivalent to 

1/r^8

200

9⁰

1

1.6 & 1.7 Continued

0

1. What do we do with the exponents when dividing the same base?

2. What do we do with different bases that have the same exponents and are being multiplied?

3. What do we do when we raise a power to a power?

1. We subtract the exponents when dividing the same bases.

2. We multiply the bases and push the exponent outside of parentheses.

3. We multiply the exponents.

100

4^10 / 4^8 

4² = 16

100

p⁴ x q⁴

(pq)⁴

200

(v⁵)¹¹

v⁵⁵

200

y^8/(y^2)^3

y^8 / y^6 = y^2