8-1 Rational Numbers

Objective: Students will be able to write rational numbers as decimals and

decimals as fractions.

8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal

expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Do Now:

Rational Numbers on a Number Line

– 4 – 3 – 2 – 1 0 1 2 3 4

| | | | | | | | |

Negative numbers Positive numbers

Zero is neither negative nor positive

Natural Numbers

Whole Numbers

Integers

Another set of numbers you can display on a number line is the set of rational numbers.

A rational number is any number that can be written in the form , where a and b are integers and b ≠ 0.

€

a

bSome examples of rational numbers:

2

1

3

25

17

3

15

11

14

1

3

99

265

5.0

A rational number can also be expressed as a decimal that terminates or as a decimal that repeats indefinitely:

2

1

3

25

17

3

15

11

14

1

3

3.0 4.3 5 27.1 3 ...676767.2

99

265

= ======

To express the rational number as a decimal, divide the numerator (top) by the denominator (bottom)

denominator numeratornumerator

denominator

Write as a decimal:

Write as a decimal:

€

5

8

€

−12

3

In a recent season, St. Louis Cardinals first baseman Albert Pujols had 175 hits in 530 at bats. What is his batting

average to the nearest thousandth?

Write 0.45 as a fraction:

Write 1.32 as a fraction:

Remember: Infinite repeating decimals are usually represented by putting a line over (sometimes under) the

shortest block of repeating decimals. Every infinite repeating decimal can be expressed as a fraction.

Challenge!

Write as a fraction:

€

0.7

1) Ask yourself, how many numbers repeat? 1 number2) Assign a variable for the decimal. Let n = 0.77777 3) Assign power of 10 times the variable (how many numbers repeat). Let 10n = 7.777774) Subtract variables and numbers.5) Solve for n.

Write as a fraction:

Write as a fraction:

€

0.5

€

2. 1 8

Glencoe Guided PracticePage 10

Homework 8-1Pages 11-12 All #’s

Exit Ticket:Write convert the decimal into a fraction or the

fraction into a decimal in simplest form:

€

1)4

5

2)55

163) −1.55

4)3.8