Lesson 1: Understanding Rational and Irrational Numbers
Standard: CC.2.1.8.E.1
Goals: Identify rational and irrational numbers.
Write decimals as fractions and fractions as decimals.
Vocab:
Rational Number:
𝑎
Any number that can be written in the form
where a is an integer and b is
𝑏
any nonzero integer. (Also, terminating decimals, repeating decimals, and
square roots of perfect squares.
Irrational Number:
Real Number:
Perfect Square:
𝑎
A number that cannot be written in the form form
where a is an integer
𝑏
and b is any nonzero integer. (π , 2.14535…, square roots of non-perfect
squares.)
All rational and irrational numbers. ( Square roots of negative numbers are NOT in
the set of real numbers.)
A number that is the square of a whole number.
(1,4,9,16,25,36,49,64,81,100,121,144,…)
Practice identifying rational and irrational numbers. Place
the given numbers into the correct circle:
Rational
16
3.5
− 25
Irrational
1.2482730…
π
1
8
2.45
−9.5
8
- 11
2.831
Writing equivalent decimal forms for numbers.
Adding zeros to the end of a decimal does not change its value.
Example: 12.4 = 12.40 = 12.400 = 12.4000
2.45 = 2.4545 = 2.454545 = 2.45454545
Writing decimals as fractions: (Helpful to read the number correctly.)
Example: 0.12 is read “12 hundredths” =
12
100
=
3
25
You try: Write the following decimals as fractions in lowest terms.
1.) 4
2.) -0.8
3.) 3.05
4.) 0.010
Converting Repeating Decimals to Fractions.
Step 1: Set n = to the decimal
Step 2: Count the number of digits that are repeating.
Step 3: If there is one repeating digit multiply n and the decimal by 10
If there is two repeating digits multiply n and the decimal by 100
and so on.
Step 4: Subtract the two equations. Then Solve for n.
Example: Write 4.63 as a fraction.
Step 1: n = 4.63
Step 2: Since there are 2 digits repeating, multiply by 100.
100n = 463.63
Step 3:
100n = 463.63
n = 4.63
-
99n = 459
n=
459
99
You try: Write 0.81 as a fraction.
7
= 4 11