Unit 2. Day 4.

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 → 1.7320508… 2. Simplifying rational numbers (fractions) makes them easier to work with and to understand 126 144 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

Yesterday Today Fraction Decimal

? ? ? ? ? ? Q: Can every decimal be transformed into a fraction? Terminating Decimals ? ? 0.64 Repeating Decimals ? ? 0. 81 0.818181… Non-terminating, non-repeating decimals ? ? 3.141592653589793…

Review of math fact #1: Any number can be a “fraction” 17 1 2.8 1 17 2.8 61 1 .0123 1 61 0.123 3 1 42.5 1 3 42.5

Review of math fact #2: Multiplying by 10, 100, 1000, etc. 1.23456 1.23456 1.23456 × 10 × 100 × 1000 12.3456 123.456 1234.56 1.23456 1.23456 × 100000 × 10000 123456. 12345.6

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

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

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

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

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*:

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

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

Example F*: Write the decimal as a fraction in simplest form. 1000 0 875 . 875 1000 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

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

Yes! ? ? Q: Can every decimal be transformed into a fraction? Terminating Decimals: 0.64 ? Repeating Decimals: 0. 81 ? Non-terminating, non-repeating decimals: 3.141592653589793…