1. Relationships Between Sets of Rational Numbers

2. Rational
Irrational
Integers
Whole
Counting numbers

3. Rational Irrational π Integers Decimal - Repeating & Terminating
Fractions
-1,-2,-3,-4 … π
Whole
Percents
1,2,3,4 ….
Counting numbers

4. Rational numbers can be written in several forms2
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

5. 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

6. 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 % ●

7. Percent to Fraction Fraction to Percent Put percent over 100 Simplify50 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

8. 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

9. - - - - - - - EX 14) , 84 %, and 0.7 , 0.7, 84% EX 15) , 84 %, and 0.73 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?

10. 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.

11. Notes

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

14. 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) =

15. 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)

16. 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) =

17. 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.

18. 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

19. EX 14) EX 15) Write the original numbers in least to greatest order
Graph the numbers on a number line.

20. Conversions you need to memorize
Fraction
Decimal
Percent
Fraction
Decimal
Percent
Any fraction with a denominator of 5,10,100.