Rational Number Systems

SBAC 8th Number Systems Review

By Alicia Nosal

​Rational / Irrational Numbers

​Rational Numbers:

​-6

​

⅓​

​

​2.4​

​ _

​8.3

​​

√81

​

⅖

Multiple Select

Choose the numbers that are rational.

• 4.56875...

• $$\sqrt[3]{8}$$  

• $$\sqrt[]{36}$$  

• $$\sqrt[]{11}$$  

Multiple Choice

Choose the number that is irrational.

• $$\frac{3}{8}$$  

• $$\sqrt[3]{27}$$  

• $$\sqrt[]{8}$$  

• $$\frac{\sqrt[]{25}}{\sqrt[]{81}}$$  

Poll

Let's take a vote!

$$\frac{1}{\sqrt[]{25}}$$  

• rational

• irrational

Poll

Let's vote!!

-3.56 is ______

• rational

• irrational

Draw

Shade in the boxes that are rational.

​Estimating Square Roots of

Non-Perfect Squares:

​Estimate √26

​

​√25 = 5

​√36 = 6

​

​26 is slightly more than 25, so

√​26≃5.1

​

​​

Multiple Choice

What are the two perfect squares above and below 15?

• 16 and 25

• 3 and 4

• 9 and 16

• 3 and 9

Multiple Choice

Estimate $$\sqrt[]{17}$$  to the nearest whole number.

• 4.1

• 4.2

• 5

• 4

Multiple Choice

Estimate $$\sqrt[]{26}\ +\ \sqrt[]{65}$$   to the nearest whole number.

• 12

• 13

• 14

• 15

​Negative Exponents

Multiple Choice

Evaluate $$6^{-3}$$  

• -6

• $$-6^3$$  

• $$\frac{1}{6^3}$$  

• -216

​Multiplying Exponents

(Same base, add the exponents)​

Multiple Choice

Evaluate $$4^2\ \cdot\ 4^5$$  

• $$4^7$$  

• $$4^{10}$$  

• $$4^3$$  

• $$16^7$$  

Multiple Choice

Evaluate $$3^8\ \cdot\ 3^{-2}$$  

• $$6^6$$  

• $$6^{-16}$$  

• $$3^{-16}$$  

• $$3^6$$  

​Dividing Exponents

Multiple Choice

Evaluate $$\frac{x^6}{x^2}$$  

• 4x

• $$x^3$$  

• $$x^4$$  

• 6x - 2x

Multiple Choice

Evaluate $$\frac{5x^3}{x^2}$$  

• 4x

• 5x

• $$5x^5$$  

• -5x

Multiple Choice

Evaluate $$\frac{2^3}{2^{-2}}$$  

• $$2^5$$  

• $$1^5$$  

• $$2^{-6}$$  

• 2

​Power to a Power

Multiple Choice

Evaluate $$\left(2^3\right)^3$$  

• $$2^6$$  

• $$8^6$$  

• $$6^3$$  

• $$2^9$$  

​Scientific Notation

Rewrite the number with a decimal so it is at least 1, but less than 10​. Count how many places to go back to the original number and multiply by that power of 10.

Multiple Choice

Write in Scientific Notation.

6,400,000

• $$6.4\ x\ 10^6$$  

• $$6.4\ x\ 10^5$$  

• $$0.64\ x\ 10^7$$  

• $$0.64\ x\ 10^6$$  

​Scientific Notation

Multiple Choice

Write in Scientific Notation.

0.00000465

• $$0.465\ x\ 10^{-5}$$  

• $$4.65\ x\ 10^{-5}$$  

• $$4.65\ x\ 10^{-6}$$  

• $$4.65\ x\ 10^{-8}$$  

​Standard Form

Multiple Choice

Write in Standard Form.

$$3.5\ x\ 10^6$$  

• 350,000

• 3,500,000

• 35,000,000

• .0000035

Fill in the Blanks

Write in standard form.

$1.45\ x\ 10^{-5}$