Rational and Irrational Numbers

Objective: I will identify rational and irrational numbers and identify repeating and terminating decimals

MAFS.8.NS.1: Know that there are numbers that are notrational, and approximate them by rational numbers.

MAFS.8.NS.1.1: 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, andconvert a decimal expansion which repeats eventually

into a rational number. (MP.2, MP.6, MP.7

Do Now• Change into decimal form. Identify if it is rational

or irrational. Explain

• 157/50

• 2/3• 5/13

Rational and Irrational Numbers

• The goal of simplifying fractions is to make the numerator and the denominator relatively prime. Relatively prime numbers have no common factors other than 1.

You can often simplify fractions by dividing both the numerator and denominator by the same nonzero integer. You can simplify the fraction to by dividing both the numerator and denominator by 3.

12 of the 15 boxes are shaded.

4 of the 5 boxes are

shaded.

The same total area is shaded.

1215

45

=1215

45

Simplifying Fractions

16

80

16 = 1 • 4 • 480 = 5 • 4 • 4

;16 is a common factor.

1 5

=

1680

Divide the numerator and denominator by 16.= 16 ÷ 16

80 ÷ 16

Simplify.

= 0 for a ≠ 0 = 1 for a ≠ 0

= = –

Remember!

0a

aa

–7 8

7 –8

7 8

= –18 29

–18 29

18 = 2 • 9 29 = 1 • 29

; there are no common factors.

18 and 29 are relatively prime.–18 29

Simplify.

Simplifying Fractions

= – 17 35

17 –35

17 = 1 • 17 35 = 5 • 7

; there are no common factors.

17 and 35 are relatively prime. 17 –35

Check It Out: Example 1B

Simplify.

A repeating decimal can be written with a bar over the digits that repeat. So 1.3333… = 1.3.

Writing Math

_

5.37

A. 5.37

7 is in the hundredths place.37 100

= 5

Writing Decimals as Fractions

Write each decimal as a fraction in simplest form.

0.622

B. 0.6222 is in the thousandths place.

622 1000

=

= 311 500

Simplify by dividing by the common factor 2.

Rational and Irrational Numbers

• Reflection: How do you change a repeating decimal into a fraction.