# Lesson 5.1 Rational Numbers Worksheet

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5.1
Rational Numbers
Now
B E F O R E
W H Y ?
You wrote decimals and
You’ll write fractions as
So you can assess a recycling
Vocabulary
fractions.
decimals and vice versa.
plan, as in Ex. 45.
rational number,
p. 219
terminating decimal,
A
rational number
is a number that
p. 219
Rational numbers
can be written as a quotient of two
repeating decimal,
Integers
p. 219
integers. Whole numbers and integers
are part of the set of rational numbers,
Whole
as shown in the Venn diagram.
numbers
Example 1
Identifying Rational Numbers
Show that the number is rational by writing it as a quotient of two
integers.
3
1
a. 7
b.
10
c. 5
d.
3
4
2
Solution
7
a. Write the integer 7 as
.
1
10
10
b. Write the integer 10 as
or
. These fractions are equivalent.
1
1
3
2
3
c. Write the mixed number 5
as the improper fraction
.
4
4
Review Help
1
1
1
7
d. Think of 3
as the opposite of 3
. First write 3
as
. Then you
2
2
2
2
For help with writing mixed
1
7
7
numbers as improper
can write
3
as
. To write
as a quotient of two integers,
2
2
2
fractions, see p. 778.
you can assign the negative sign to either the numerator or the
7
7
denominator. You can write
or
.
2
2
If you take a rational number in the
Terminating and Repeating Decimals
a
form
and carry out the division of a by b, the quotient will be either a
b
terminating decimal or a repeating decimal. In a
terminating decimal
,
the division ends because you obtain a final remainder of zero. In a
repeating decimal
, a digit or block of digits in the quotient repeats
without end. Example 2 on page 220 shows how to write both a
terminating decimal and a repeating decimal.
219
Lesson 5.1
Rational Numbers