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**Relationships Between Sets of Rational Numbers**

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Rational Irrational Integers Whole Counting numbers

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**Rational Irrational π Integers Decimal - Repeating & Terminating**

Fractions -1,-2,-3,-4 … π Whole Percents 1,2,3,4 …. Counting numbers

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**Rational numbers can be written in several forms**

2 1 +1 2 - 0 2*1 2/1 4/2 8/4 2.0 200% -(-2) Most common Simplified fraction Decimal Percent Not in notes

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**Convert between decimal fraction and percent**

Decimal to Fraction Unit ● tenths hundredths thousandths 1. Place decimal digits over the place value 5 EX 1) .5 = 10 2. simplify 5 10 ÷ 5 1 2 = ÷ 5 5 1 20 EX 2) 0.05 = = 100 5 1 200 EX 3) 0.005 = = 1000

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**Out of sight to the right**

Decimal to Percent 1. Move decimal two places right 2. Add zeroes if necessary EX 4) 5 = 50 % ● EX 5) 2 5 = 250 % 3. Add percent to answer ● = 300 % EX 6) 3 Out of sight to the right ● Percent to Decimal 1. Move decimal two places left EX 7) 2. Add zeroes if necessary 5 % = 0.05 ● 3. Remove percent sign from answer EX 8) = 0.025 2 5 % ●

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**Percent to Fraction Fraction to Percent Put percent over 100 Simplify**

50 5 1 EX 9) 50 % = = = 100 10 2 1 450 45 9 = 4 EX 10) 450 % = = = 2 100 10 2 Fraction to Percent Make fraction a decimal Turn decimal into a percent 1 EX 11) = .2 = 20 % 5 1 EX 12) 3 = 3.2 = 320 % 5

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**Order from least to greatest.**

4 5 1. Change all numbers to percents EX 13) 0.93, and 90 % , 80 % 90 % 93 % Graph the numbers on a number line. 4 5 0.93 90 % Write the original numbers in least to greatest order 4 5 , 90 %, 0.93

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**- - - - - - - EX 14) , 84 %, and 0.7 , 0.7, 84% EX 15) , 84 %, and 0.7**

3 5 Write the original numbers in least to greatest order EX 14) , %, and 0.7 60 % 84 % 70 % 3 5 , 0.7, 84% - - - 3 5 EX 15) , %, and - - - 60 % 84 % 70 % - 3 5 Graph the numbers on a number line. - 84%, - 0.7, LEAST GREATER What do you notice between the two examples above?

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**Conversions you need to memorize**

Fraction Decimal Percent 1 1.0 100 .25 25 0.5 50 3/4 0.75 75 1/8 0.125 12.5 5/8 0.625 62.5 1/5 0.2 20 4/5 0.8 80 Fraction Decimal Percent 1/10 0.1 10 2/10 0.2 20 1/25 0.04 4 1/50 0.02 2 1/100 0.01 1 1/3 0.33 33 1/3 2/3 0.66 66 2/3 Any fraction with a denominator of 5,10,100.

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Notes

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**Convert Rational Numbers**

Date _______________ Convert Rational Numbers Any number that can be expressed as a fraction of two integers

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**Convert between decimal fraction and percent**

Decimal to Fraction Unit ● tenths hundredths thousandths 1. Place decimal digits over the place value EX 1) = 2. simplify ÷ = ÷ EX 2) = EX 3) =

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**Decimal to Percent Percent to Decimal EX 4) EX 5) EX 6) EX 7) EX 8)**

1. Move decimal ___ places _____ 2. Add ______ if necessary EX 4) EX 5) 3. Add _______ to answer EX 6) Percent to Decimal 1. Move decimal ___ places ____ EX 7) 2. Add ______ if necessary 3. ______ percent sign from answer EX 8)

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**Percent to Fraction Fraction to Percent Put percent over ___ Simplify**

EX 9) = EX 10) = Fraction to Percent Make fraction a _______ Turn _______ into a ______ EX 11) = EX 12) =

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When rational numbers are written in a variety of forms, you can compare the numbers by writing them all in the same form. The values on a number line increase as you move from left to right.

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**Order from least to greatest.**

1. Change all numbers to __________ EX 13) Graph the numbers on a number line. Write the original numbers in least to greatest order

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**EX 14) EX 15) Write the original numbers in least to greatest order**

Graph the numbers on a number line.

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**Conversions you need to memorize**

Fraction Decimal Percent Fraction Decimal Percent Any fraction with a denominator of 5,10,100.

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