Rational Numbers Juan, Billy, and Charlene participated

in a one minute pie-eating contest with 25 contestants. The trio came in the top three. Juan ate 3/5 of his pie, Billy ate 5/9 of his pie, and Charlene ate 4/7 of her pie. What place did each of them finish? Explain your answer without using a calculator. You can draw a picture if needed.

ANSWER(1) Juan 0.6(2)Charlene

0.571428571428571428571428(3) Billy

0.5555555555555555555555555555

What do notice about answers #2 and #3.They are repeating decimals while the

answer for #1 is a terminating decimal.

Rational Numbers Common Core #1 Continued

Understand that every number has a decimal expansion and for

rational numbers show that each decimal expansion terminates or eventually repeats.

To change a fraction into a decimal, you divide the NUMERATOR by the DENOMINATOR.

For example, to change into a decimal, you would

divide the 3 by the 4.4

3

344

3 0.34

0.7

-2 8 20

5

-2 0 0

75.04

3

This is called a TERMINATING DECIMAL. (it comes to an end, as in terminate a game!)

To change a fraction into a decimal, you divide the NUMERATOR by the DENOMINATOR.

Write each fraction or mixed number as a decimal.

20

70.720

0.3

-6 01 00

5

-1 0 0 0

35.020

7

This is called a TERMINATING DECIMAL. (it comes to an end, as in terminate a game!)

To change a fraction into a decimal, you divide the NUMERATOR by the DENOMINATOR.

Write each fraction or mixed number as a decimal.

3

13.0...333.0 0.13

0.3

- 9 1 0

3

- 9 1 0

3……..

- 9 1

This is called a REPEATING DECIMAL. (a pattern in the digits repeats forever!)

To change a fraction into a decimal, you divide the NUMERATOR by the DENOMINATOR.

Write each fraction or mixed number as a decimal.

4

35 75.5

4

35

Memorizing some conversions like these will make things a lot EASIER!

We already know that ¾ =

0.75

¼ = 0.25 ½ = 0.50 ¾ = 0.75 (one quarter) (half of a dollar) (three quarters)

To change a fraction into a decimal, you divide the NUMERATOR by the DENOMINATOR.

Write each fraction or mixed number as a decimal.

8

32 375.2

8

32 0.38

0.3

-2 4 6 0

7

- 5 6 4 0

5

- 4 0 0

Notebook/Board ExamplesConvert the following fractions to decimals(1) (2) (3) (4) (5)

7

23

8

5

24

12

9

44

11

To change a decimal into a fraction, you place the decimal number over the correct pace value position as a fraction ( #/10 #/100 #/1000)

For example, to change 0.25 into a fraction, you

would place 25 over a denominator of 100 since it

is read “twenty-five hundredths”.

25/100 = 1/4

Lets convert 0.6 to a fraction in simplest form

How do you say 0.6?

“six-tenths”

So 6/10 or 3/5 in simplest form

Lets convert 3.345 to a fraction in simplest form

How do you say 3.345?

“Three and three-hundred-forty-five thousandths”

So 3 345/1000 in or 3 69/200 in simplest form

You try these 3 for your Notebook Examples

(1)0.68 (2) 1.22 (3) -0.875

Answers

(1)17/25

(2) 1 11/50

(3) -7/8

BIG DOG QUESTIONWrite the following decimal as a fraction:

-8.3713713713713173171371371……………………………………….

Answer is -8 371/999