Test 2: The Number System

Test 2: The Number System

Study Guide - Review

​Classifying Real Numbers

​Rational Numbers

Can be written as a fraction

​

• Natural Numbers (Counting Numbers)

• Whole Numbers

• Integers

​

​What does this mean: Positive whole numbers, Zero, Negative whole numbers, fractions, mixed numbers, perfect square roots, repeating decimals and terminating decimals are all Rational Numbers.

​Irrational Numbers

​Cannot be written as a fraction

​

Decimals that does not terminate or repeat.

• ​Non-terminating decimals

• ​Non-repeating decimals

​

Hint:​

• Imperfect Squares

• Anything with

​

​Examples:

• ​9.7658128....., -7.109823...., , , , ,

Multiple Select

Select all that are true. Zero is a ___________.

• whole number

• natural number

• integer

Multiple Choice

The set of numbers {-3, -2, -1, 0, 1, 2, 3} are called?

• whole numbers

• integers

• rational numbers

• natural numbers

Multiple Choice

True or False: -10 is a whole number

• True

• False

Multiple Select

Select all that apply. 120 is a _________.

• whole number

• integer

• natural number

Multiple Choice

True or False: -43 is an integer

• True

• False

Multiple Select

Select all that apply. -14 could NOT be which type of number?

• integer

• whole number

• natural number

Multiple Choice

The set of numbers {1, 2, 3, ...} are called?

• whole numbers

• integers

• natural numbers

Multiple Choice

Which of the following can be classified as a whole number?

• -3.5

• $$\frac{5}{4}$$

• 245

• 0.66

Multiple Choice

In what category does  $$\frac{6}{11}$$   belong ?

• Integer

• Natural Number

• Rational Number

Multiple Choice

Which number is a Rational Number?

• $$\sqrt[]{17}$$  

• $$\sqrt[]{144}$$  

• $$2\pi$$  

• $$4+\pi$$  

Multiple Choice

Which number is a Rational Number?

• $$\sqrt[]{80}$$  

• $$\frac{5}{\pi}$$  

• 7.9432840.......

• $$-6.5$$  

Multiple Choice

Which number is an Irrational Number?

• $$\sqrt[]{81}$$  

• $$7.333333$$  

• $$3\pi$$  

• $$55\ \frac{1}{2}$$  

Multiple Choice

Which number is an irrational number?

• $$-\sqrt[]{95}$$  

• $$\sqrt[]{64}$$  

• 7.8

• 0

Multiple Choice

Classify  $$\sqrt{5}$$  

• Rational

• Irrational

Multiple Choice

Classify  $$-3.254$$  

• Rational

• Irrational

Multiple Choice

Classify  $$\frac{\pi}{2}$$  

• Rational

• Irrational

Multiple Choice

Classify  $$\frac{5}{0}$$  

• Rational

• Irrational

• Not a Real Number

Multiple Select

Real numbers consist of :

• Rational Numbers

• Irrational Numbers

• Arbitrary Numbers

Multiple Select

The following are examples of Integers

• (1/2, -3, 4, .75)

• (.987, .786, -9.9)

• (1,-1,2,-2,3,-3)

Multiple Choice

Is $$\frac{0}{3}$$  rational, irrational or not a real number?

• Rational

• Irrational

• Not a Real Number

Multiple Choice

Is   $$.\overline{11}$$    rational or irrational?

• Rational

• Irrational

Multiple Choice

Is $$\sqrt{-64}$$  rational or irrational?

• Rational

• Irrational

• Not a Real Number

Multiple Choice

Is $$\sqrt{40}$$  rational or irrational?

• Rational

• Irrational

Multiple Select

Select all that are rational numbers

• 0.24

• -14.2

• $$2\ \frac{1}{5}$$

• $$-\frac{5}{6}$$

• $$0.\overline{3}$$

Multiple Select

Select ALL the Irrational Numbers

• $$\sqrt{15}$$  

• $$\Pi$$  

• $$\sqrt{37}$$  

Multiple Choice

$$-6,\ 0.\overline{5}\ ,\ and\ 3.75$$  are ALL examples of rational numbers

• True 

• False

Multiple Choice

$$\frac{5}{9},\ -\frac{9}{4},\ -3\ \frac{2}{7}$$  are ALL examples of rational numbers

• True 

• False

Multiple Choice

$$\sqrt{9},\ \sqrt{25},\ \sqrt{40}$$  are ALL examples of rational numbers

• True 

• False

Multiple Choice

$$\frac{\sqrt{20}}{9}$$  

• Rational

• Irrational

Multiple Choice

$$\frac{\sqrt{64}}{12}$$  

• Rational

• Irrational

Multiple Choice

$$4\ \frac{3}{5}$$  

• Rational

• Irrational

​Squares, Cubes, and Estimating Square Roots

Multiple Choice

What is 12²?

• 24

• 144

• 14

• 6

Multiple Choice

What is 7²?

• 9

• 3.5

• 14

• 49

Multiple Choice

(-6)²

• 12

• -12

• -36

• 36

Poll

Squaring a number is just like multiplying by 2.

For example: Does 5² = 5 x 2

• not sure

• true

• false

Multiple Choice

$$\sqrt{16\ }$$  = ?

• 8

• 32

• 4

• 2

Multiple Choice

$$\sqrt{49}$$  = ?

• 24.5

• 98

• 2

• 7

Multiple Choice

Evaluate √36

• 6

• -9

• 18

• -18

Multiple Choice

Find the best estimate for √18 . Look at the number line.

• 4.2

• 4.4

• 5.1

• 4

Multiple Choice

Round to the Nearest Tenth: √28

• 5.6

• 5.9

• 5.3

• 8

Multiple Choice

Point B could represent which of the following numbers?

• √24

• √30

• √35

• √42

Multiple Choice

The √40 is between which two consecutive whole numbers?

• 7 & 8

• 4 & 5

• 5 & 6

• 6 & 7

Multiple Choice

Between which two consecutive whole numbers is the√200? 

• 13 and 14

• 15 and 16

• 14 and 15

• 11 and 12

Multiple Choice

What number, n, cubed is equal to 64?

n³ = 64

• 4

• 2

• 8

• 262,144

Multiple Choice

Which number is both a perfect square and a perfect cube?

• 64

• 27

• 81

• 16

Multiple Choice

Evaluate ∛1

• 1

• 2

• 3

• 4

Multiple Choice

∛125

• 5

• 4

• 6

• 7

Multiple Choice

Evaluate. 7³

• 313

• 323

• 333

• 343

Multiple Choice

What is the cube root of 27?

• 9

• 3

• -3

• -9

Multiple Choice

∛216

• 6

• 72

• 108

• 4

Multiple Choice

In 2³ what is the base?

• 2

• 3

• 2³

Multiple Choice

What is -9 cubed?

(-9)³

• -729

• 729

• 27

• -27

Multiple Choice

The number 512 is a perfect cube because 512 = 8³.

Which number below is also a perfect cube?

• 125

• 300

• 150

• 256

Multiple Select

Identify each value that is a perfect cube:

• 27

• 1,000

• 90

• 1

Multiple Choice

Find the cube root of -1,331:

• -121

• -11

• -443.67

Multiple Choice

A cube with side length s has a volume of 64 cubic units. What is the length of the side of the cube?

• 32 units

• 16 units

• 8 units

• 4 units

Multiple Choice

Find the volume of a cube if its length is 3cm

• $$9cm^3$$

• $$27cm^3$$

​Fractions, Decimals, and Percentages

Changing a Percent to a Fraction

-Put the Percent in the numerator

-Put 100 in the denominator

-You can reduce the fraction too!

Multiple Choice

What is 79% as a fraction?

• 7/9

• 79/79

• 79/100

• 1/3

Reducing Percents

• If the fraction can be reduced:

• Divide top and bottom by a common factor (GCF)

Multiple Choice

The fraction

$$\frac{60}{100}$$   can be divided by?

• 8

• 12

• 3

• 20

Multiple Choice

Reduce the fraction

$$\frac{15}{100}$$  

• $$\frac{3}{100}$$  

• $$\frac{3}{20}$$  

• $$\frac{5}{20}$$  

• $$\frac{3}{5}$$  

Divide by 5

Both 15 and 100 are divisible by 5

Fill in the Blank

Put the percent in simplest fraction form:

$$25\%$$  

Multiple Choice

7/8 as a decimal

• 0.958

• 0.875

• 0.739

• 0.856

Multiple Choice

2/9 as a decimal

• 0.2222...

• 0.22

• 0.2

• 0.222

Changing a Percent to a Decimal

Move the decimal Point

• Always move the decimal 2 spots to the LEFT

Multiple Choice

Write the percent as a decimal 65%

• 0.65

• 6.5

• 65

• 650

Multiple Choice

What is 70% turned into a decimal?

• 0.70

• 7.0

• 70.0

• .007

Multiple Choice

Which is the decimal for 3.5%?

• 3.5

• 0.35

• 0.0035

• 0.035

Multiple Choice

Change 4% to a decimal.

• .04

• .004

• .4

• 4

​Comparing and Ordering Numbers

Multiple Choice

Which symbol would you use to make this statement true?

0.90 _____ 0.9

• <

• >

• =

Multiple Choice

Howard studied math for 0.75 hour. Carol studied math for 0.80 hour. Who studied math for the greater amount of time?

• Howard

• Carol

Multiple Choice

Which symbol would you use to make this statement true?

0.15 _____ 0.8

• <

• >

• =

Multiple Choice

Emily bought the following amounts of fruit at a fruit stand: 0.75 pounds of grapes 0.5 pounds of bananas 1.25 pounds of apples Which fruit weighs the least?

• Grapes

• Bananas

• Apples

• Fruit Salad

Multiple Choice

Which decimal is the smallest? 0.56 0.65 0.605 0.506

• 0.56

• 0.65

• 0.605

• 0.506

Multiple Choice

Which list of numbers is in order from least to greatest?

• A √23, 5, 6, 43%

• B 5, √23, 6, 43%

• C 43%, 5, √23, 6

• D 43%, √23, 5, 6

Multiple Choice

Order these racers from greatest to least:

Driver A = 145.155 mph

Driver B = 145.827 mph

Driver C = 144.809 mph

• C, B, A

• B, A, C

• C, A, B

Multiple Choice

Order from Greatest to Least 1.876, 1.77, 1.80

• 1.876, 1.80, 1.77

• 1.80, 1.77, 1.876

• 1.876, 1.77, 1.80

• 1.80, 1.77, 1.876

Multiple Choice

Order from Least to Greatest 3.471, 2.610, 1.544, 2.002

• 2.002, 2.610, 1.544, 3.471

• 1.544, 2.610

• 3.471, 2.610, 1.544, 2.002

• 1.544, 2.002, 2.610, 3.471

Multiple Choice

Tammy, Kelley, and Jim love reading books. Tammy read 7.75 hours last month. Kelley read 7.69 hours. Jim read 7.075 hours. Who spent the most time reading?

• Tammy

• Kelley

• Jim

• Both A and C

Multiple Select

Choose all of the numbers that are greater than 50%.

• $$\frac{4}{5}$$

• 0.09

• 0.6

• $$\sqrt{16}$$

• $$\frac{4}{9}$$

Multiple Choice

Place numbers from least to greatest.

• -3/7, -0.44, √2, 0.14, 141%,

• -0.44, 0.14, -3/7, √2, 141%

• -3/7, -0.44, 0.14, 141%, √2

• -0.44, -3/7, 0.14, 141%, √2

Multiple Choice

Order 3π, √ 10 , and 3.25 from least to greatest.

• √ 10, 3π, 3.25

• √ 10, 3.25, 3π

• 3π, 3.25, √ 10

•  3.25, √ 10, 3π

Multiple Choice

Which list shows these numbers in order from least to greatest?