Real Numbers Worksheet Page 2
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1
2
3
4MAP
Mathematics Achievement Program
SFSU – High School Collaborative
Example 3:
Let a = 4 and b = 7. Plot a and b on a number line, find the distance
a − .
between a and b, and compute
b
The distance between 4 and 7 is 3 units (see the number line below) and
a −
4 −
−
b
=
7
=
3
= 3.
7
8
3
4
5
6
_______________________________________________________________________
For exercises 12-15, plot a and b on a number line, find the distance between a and b, and
a − .
compute
b
12. a = 6 and b = 5
13. a = – 3 and b = 8
14. a = –5 and b = – 2
a −
15. If a and b are any real numbers, what does
b
represent on the number line?
________________________________________________________________________
Every real number has a decimal representation. For example, the decimal
1
representation of
is 0.5, which is a finite (terminating) decimal. Some real numbers,
2
however, have an infinite (non-terminating) decimal representation. For instance,
2
=
K
0
6 .
. 0
666
. We sometimes write 0.666 … as
to indicate the repeating pattern.
3
________________________________________________________________________
For exercises 16-19, find the decimal representation of the fraction.
2
22
5
9
16.
17.
18.
19.
5
8
3
11
________________________________________________________________________
Example 4:
Write 0.56 as a fraction in reduced form.
56
23
=
=
Since 0.56 is 56 hundredths, we have
. 0
56
.
100
50
________________________________________________________________________
For exercises 20-23, write the decimal as a fraction in reduced form.
20. 0.3
21. 0.68
22. 0.214
23. 0.1075
24. Can every terminating decimal be written as a fraction? Explain.
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