Real Number System Review

​The Real Number System

• ​Real Numbers include both

  • rational and

  • irrational numbers

• ​Rational Numbers include:

  • Natural, Whole, Integers, Fractions, Repeating and Terminating Decimals

• ​Irrational numbers are those numbers that cannot be represented as a fraction or repeating or terminating decimal

  • ​pi

  • ​square root of any non-perfect square

Multiple Select

$$\sqrt{20}$$  

Be sure to choose all classiications...

• irrational

• rational

• integer

• whole number

• real number

Multiple Select

$$\pi$$  

Be sure to choose all that apply.

• irrational

• real

• integer

• whole number

• natural number

Multiple Select

$$\frac{1}{3}$$  

Be sure to choose all that apply...

• irrational

• rational

• integer

• real number

• natural number

Multiple Select

• irrational

• rational

• integer

• whole number

• real number

Multiple Select

$$\sqrt{25}$$  

Be sure to choose all that apply...

• irrational

• rational

• integer

• whole number

• natural number

Multiple Select

$$0$$  

Be sure to choose all that apply...

• irrational

• rational

• integer

• whole number

• natural number

Multiple Select

Check all subsets that -7 belongs to.

• Irrational

• Rational

• Integers

• Whole

• Natural

Multiple Select

Square roots of perfect squares are always _____ numbers.

• irrational

• rational

Multiple Choice

$$\sqrt{16}$$  is included in the set of _______ because it simplifies to 4.

• irrational numbers

• natural numbers

Multiple Choice

-1.4 is not included in the set of ______ because it has a decimal (or fractional) part.

• rational numbers

• integers

• real numbers

​Converting Fractions, Decimals and Percents

• ​Convert fraction to decimal - divide numerator by denominator

• ​Convert decimal to percent - move decimal 2 places to the right

• ​Convert fraction to percent -

  • ​convert the fraction to a decimal

  • ​convert the decimal to a percent

• ​Convert decimal to fraction

  • ​if non-repeating decimal

    • ​make the numerator a whole number

    • ​make the denominator 10, 100, 1000, etc.

  • ​if repeating decimal

    • ​make the numerator the repeating decimal

    • ​make the denomiaotor 9, 99, 999, etc.

Multiple Choice

Write 33% as a fraction in simplest form.

• 33/100

• 16/50

• 17/50

• 3/10

Multiple Choice

Write 2% as a fraction in simplest form.

• 2/100

• 1/50

• 1/5

• 2/10

Multiple Choice

Write 2/5 as a percent.

• 25%

• 20%

• 40%

• 5%

Multiple Choice

Convert to a decimal:

5/6

• 0.83

• 1.2

• 0.83 repeating

• .56 repeating

Multiple Choice

Convert to a percent:

0.35

• 35/100

• 0.035%

• 35%

• .35%

Multiple Choice

Change to a fraction

0.018

• 18/1000

• 9/500

• 4/250

• 18/100

Multiple Choice

Convert to a decimal

2/11

• 0.18 repeating

• .211

• .11

• .18

​Powers & Exponents

​A power consists of a base and an exponent

Multiple Choice

In the expression 2⁵, what is the BASE?

• 2
• 5

Multiple Choice

Evaluate: 7³

• 21

• 343

• 7 x 7 x 7

• 7 x 3

Multiple Choice

Write in exponential form: 3 x 3 x 3 x 3

• 3 x 4

• 3⁴

• 81

• 3²

Multiple Choice

Write the product as a power:              

 9 x 9 x 9

• 729
• 27
• 9³
• 3⁹

Multiple Select

Select ALL of the following that are equivalent to 5×5×5

• five cubed

• five squared

• 5³

• 3⁵

• 125

​Estimating Square Roots

Multiple Choice

In between what two integers is the square root of 77?

• 5 and 6
• 6 and 7
• 7 and 8
• 8 and 9

Multiple Choice

Estimate the square root to the nearest tenth

• 8.3

• 8.9

• 9.3

• 10.3

Multiple Choice

Estimate the square root to the nearest tenth

• 3.2

• 2.9

• 3.8

• 4.2

​Comparing & Ordering Real Numbers

• ​Convert square roots and fractions to decimals

• ​Order the decimals in ascending or descending order

• ​Make sure to write the order using the original form of ratinal numbers

Multiple Choice

Put the following numbers in order from

least to greatest.

2/5, 25/10, -250

• 2/5, 25/10, -250

• -250, 25/10, 2/5

• 25/10, 2/5, -250

• -250, 2/5, 25/10

Multiple Choice

Order 5/8, 0.5, 58.3% from greatest to least.

• 5/8, 0.5, 58.3%
• 5/8, 58.3%, 0.5
• 58.3%, 5/8, 0.5
• 58.3%, 0.5, 5/8

Multiple Choice

Order from least to greatest.

• √45, 9, 6, √63

• 6, √45, √63, 9

• 6, √45, 9, √63

• √45, √63, 6, 9

​Scientific Notation

• ​Makes large and small numbers easier to understand

  • ​positive exponent - large numbers

  • ​negative exponent - small numbers

• ​Only one number to the left side of the decimal

• ​Exponent is the number of times the decimal is moved

Multiple Choice

Write 3.5 x 10⁶  in standard notation.

• 0.0000035
• 35,000,000
• 3,500,000
• 0.00000035

Multiple Choice

Write 0.00000054 in scientific notation.

• 54 x 10⁸
• 5.4 x 10⁷
• 54 x 10^-8
• 5.4 x 10^-7

Multiple Choice

Write 3.629 x 10⁷          in standard notation.

• 36,290,000,000
• 36,290,000
• 0.00000003629
• 0.00003629

Multiple Choice

Write 5,890,000,000 in scientific notation.

• 5.89 x 10⁹
• 0.589 x 10¹⁰
• 589 x 10⁷
• 5.89 x 10^-9

Multiple Choice

Write 0.000009 in scientific notation.

• 9 x 10^-6
• 9 x 10⁶
• 0.9 x 10^-5
• 0.9 x 10⁵