Name:
Period:
Date:
GPA 3-1, 3-2
3-1, 3-2 Fractions, Decimals, and Rational Numbers
Rational Number – any number that can be written as a fraction
(whole numbers, integers, fractions, mixed numbers, terminating or repeating decimals)
Natural Numbers (counting numbers)
Whole Numbers
Integers
– {1, 2, 3,…}
– set of natural numbers and 0 {0, 1, 2, 3,…}
– set of positive and negative whole numbers including 0 {…, -3, -2, -1, 0, 1, 2, 3,…}
Terminating Decimals – when division ends with a remainder of zero
Repeating Decimals – when one or more digits to the right of the decimal point repeat (use bar notation to show the
digits in the decimal that repeat)
I. Convert repeating decimals to fractions:
1 digit repeats
2 digits repeat
3 digits repeat
𝒓𝒆𝒑𝒆𝒂𝒕𝒊𝒏𝒈 𝒅𝒊𝒈𝒊𝒕
𝟗
𝒓𝒆𝒑𝒆𝒂𝒕𝒊𝒏𝒈 𝒅𝒊𝒈𝒊𝒕𝒔
𝟗𝟗
𝒓𝒆𝒑𝒆𝒂𝒕𝒊𝒏𝒈 𝒅𝒊𝒈𝒊𝒕𝒔
𝟗𝟗𝟗
Ex. 0. 3
Ex. 0. 42
Ex.
𝒅𝒊𝒈𝒊𝒕
2 digits
3 digits
𝟏𝟎
𝒅𝒊𝒈𝒊𝒕𝒔
𝟏𝟎𝟎
𝒅𝒊𝒈𝒊𝒕𝒔
𝟏𝟎𝟎𝟎
and 0.28
Ex. 0. 321
II. Convert terminating decimals to fractions: write the
fraction the way that you should read the decimal
1 digit
IV. Comparing fractions and decimals: change all
numbers to decimals lining up the digits vertically by
decimal and place value or convert all numbers to
fractions and get a common denominator
V. Comparing fractions only: use the cross product
(heart method)
Ex. 0.3
Ex. 0.42
Ex. 0.321
III. Convert fractions to decimals: use long division with
the numerator (top number) on the inside, denominator
(bottom number) on the outside
Ex.
Homework: GPA p. 127 (16-50 even, omit 40); GPA p. 133 (1-6 all, 22-54 even, omit 50)
Name:
Period:
Date:
GPA 3-1, 3-2
Ex. 1: Write each fraction as a decimal.
A.
C. −
B.
Ex. 2: Replace each
A.
W
i
t
h
with <, >, or = to make a true sentence. ***Must compare using the same form.
W
i
t
h
B. −
−6.4
W
i
t
h
Ex. 3: Write each number as a fraction.
B. 82
A. 3
C. −7
Ex. 4: Write each decimal as a fraction or mixed number (no improper). ***Must reduce!!!
A. 0.91
B. 6. 5
C. 0. 6
D. 13.006
Ex. 5: Identify all sets (groups of numbers) to which each number belongs.
A. −5.075
B. 𝜋
C. 3
Homework: GPA p. 127 (16-50 even, omit 40); GPA p. 133 (1-6 all, 22-54 even, omit 50)
D. −