Section 7.1 - Decimals Page 2
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1
2Chapter 7. Section 1
Page 2
• Example, page 273 number 2b. Write 34.007 as a fraction and in expanded form
7
34007
+
=
34.007 =
34
1000
1000
1
= × + + ×
34.007 3 10 4 7
1000
• Example, page 273 number 3b. Write seven hundred forty six thousand and seven hundred for six
millionths as a decimal numeral
6
746 millionths = 746/10
746,000.000746
• Example, page 273 number 4b. Write 7,589.12345 in words
seven thousand five hundred eighty nine and
twelve thousand three hundred forty five hundred thousandths
5
NOTE: hundred thousandths because it is 12345/10
Terminating Decimals:
• A fraction in simplest form is a terminating decimal if and only if the denominator has only 2s and
5s in its prime factorization
• If the prime factorization has any values other than 2s and 5s in it's prime factorization, it is a
nonterminating or repeating decimal
• Example
1/3 is a repeating decimal
⋅
⋅
⋅
3
11
9
16
2 3 7 11
• Example, page 273 number 5b. Is
a terminating decimal?
⋅
⋅
13
9
7
7 11 5
⋅
⋅
⋅
⋅
⋅
3
11
9
16
3
11
7
2 3 7 11
2 3 11
=
. No, it has a 7 in the denominator
⋅
⋅
⋅
13
9
7
4
7
7 11 5
7 5
• Example, page 273 number 6. Decide which fractions terminate, and if they do, in how many places
1
. No
11
⋅
4
17
17
17 2
272
=
=
=
. Yes. Terminates in 4 places, because that is the highest power
⋅
4
4
625
5
(5 2)
10000
3
3
3
=
=
. Yes. Terminates in 9 places, because it is the highest power
⋅
⋅
2
7
2
9
12800
10 2
5 2
17
. Yes. Terminates in 23 places, because it is the highest power
5 ⋅
19
23
2
4 3 2
• Example, page 273 number 7b. Order the fractions
by changing to decimals
,
,
11 7 5
4
=
0.36
11
2
=
0.4
5
3
=
0.428571428...
7
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