1. Unit 2. Day 4.

2. Our Rational Number Story
1. Rational numbers are numbers that can be written as ratios (without decimals) 1
42 100
2 3 −4 3 →
.42 → …
2. Simplifying rational numbers (fractions) makes them easier to work with and to understand
2∙3∙3∙7 2∙2∙2∙2∙3∙3
7 8 = =
3. Change format of rational numbers: fraction  decimal . 7 5
3 4 4 3 . −
2 8 2 − 20

3. Yesterday
Today
Fraction
Decimal

4. ? ? ? ? ? ? Q: Can every decimal be transformed into a fraction?
Terminating Decimals
? ?
0.64
Repeating Decimals
? ?
0. 81 …
Non-terminating, non-repeating decimals
? ? …

5. Review of math fact #1: Any number can be a “fraction”
17 1
2.8 1 17
2.8
61 1 61
0.123
3 1
42.5 1 3
42.5

6. Review of math fact #2: Multiplying by 10, 100, 1000, etc. × 10 ×
100 ×
1000 ×
100000 ×
10000

7. Review of math fact #3: Multiplying by 1 is legal−7 1 = −7 1
4 5
4 5 = 1 4
2 3
8 12 = 4

8. Example A: Write the decimal as a fraction in simplest form.10
0 4 .
4 10
2∙2
2 5
0.4
0.4 = = = = 1 .
2∙5 10 4 2 2
4 10
tenths
place 10 2 5

9. Example B: Write the decimal as a fraction in simplest form.
100
0 65 .
65 100
13 20
5∙13
0.65
0.65 = = = = 1 .
2∙2∙5∙5
100
65 100
100 65 4 25
hundredths
place 5 13 2 2 5 5

10. Example C: Write the decimal as a fraction in simplest form.
1000
0 375 .
3∙5∙5∙5
0.375
0.375 = = = 1 .
2∙2∙2∙5∙5∙5
1000
3 8 =
1000
375 10
100
thousanths
place 15 25 10 5 10 2 3 5 5 5 2 5 2 5

11. Write the decimal as a fraction in simplest form.
0.32
Example D*:
−0.6
Example E*:
875
0.875
Example F*: 25 35
−1.25
Example G*:

12. Example D*: Write the decimal as a fraction in simplest form.
100
0 32 .
32 100
8 25
2∙2∙2 ∙2 ∙2
0.32 = = = =
2∙2∙5∙5 1 .
100 32
100 4 8 4 25 2 2 2 4 2 2 5 5 2 2

13. Example E*: Write the decimal as a fraction in simplest form.10
−0 6 .
−6 10
−1∙2∙3
−3 5
−0.6 = = = = 1 .
2∙5 10 −
6 10
2∙3
3 5 − = =
2∙5 −6 −1 6 10 2 3 2 5

14. Example F*: Write the decimal as a fraction in simplest form.
1000
0 875 .
5∙5∙5∙7
0.875 = = = 1 .
2∙2∙2∙5∙5∙5
1000
7 8 =
1000
875 10
100 25 35 10 2 5 10 5 5 5 7 2 5 2 5

15. Example G*: Write the decimal as a fraction in simplest form.
100
−1 25 . −
−5 4
−1∙5∙5∙5
−1.25 = = = =
2∙2∙5∙5 1 .
100 −
5 4
−125
5∙5∙5 − = =
2∙2∙5∙5
100 −1
125 4 25 5 25 2 2 5 5 5 5

16. Yes! ? ? Q: Can every decimal be transformed into a fraction?
Terminating Decimals:
0.64 ?
Repeating Decimals:
0. 81 ?
Non-terminating, non-repeating decimals: …