Download Decimal Conversions

Decimal Conversion
Topic: Number Sense: Decimals
Source: Multiple
Materials: transparent one hundred grid.
Objective(s): Make connections between fractions, decimal numbers and percents.
AZ Math Standards Performance Objectives (samples):
Strand 1: Number Sense and Operation
Concept 1: Number Sense
 Grade 4 PO 16: Order three or more decimals.
 Grade 5 PO 7: Order whole numbers, fractions, and decimals.
 Grade 4 PO 17: Express fractions as terminating or repeating decimals.
Directions:
Fractions and decimals are closely related. By turning a fraction into a division problem
(numerator divided by denominator), the fraction can be represented as a decimal.
1
2
Consider the fraction . The decimal representation of
1
is 0.5 since 1  2  0.5 .
2
It is always possible to convert a fraction to a decimal. Is it ever possible to convert a
decimal to a fraction? Yes!
“Special K Method” (for converting repeating decimals to fractions):
Consider the repeating fraction 0.34 .
Let n = 0.34 . Thus 100n = 34.34 .
Then subtract the two equations: 100n = 34.34
– n = 0.34
___________
99n = 34
So… n =
34
99
.
Recall that n = 0.34 as well. And so 0.34 =
34
99
.
Decimal Conversion 1
Decimal Conversion
1. Divide the numerator by the denominator in order to convert each fraction to its
decimal form and say whether the decimal is repeating or terminating. You may
use a calculator.
(a)
21
45
=__________________
(b)
62
125
(c)
63
90
=__________________
(d)
7
30
(e)
39
60
=__________________
(f)
4
15
=__________________
=__________________
=__________________
2. Investigate the prime factorization of each simplified fraction to develop a rule for
when the decimal representation of a fraction will repeat and when it will
terminate.
Fraction
Reduced Fraction
Prime Factorization
of Denominator
Terminate or
Repeat?
21
45
62
125
63
90
7
30
39
60
4
15
Rule:_____________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
Decimal Conversion 2
3. A student says that the fraction
42
150
should be a repeating decimal because the
factors of the denominator include a 3 as well as 2’s and 5’s. But on her
calculator 42 150 seems to terminate. How would you explain this?
4. Decimals can be either rational numbers or irrational numbers. Decimals that
______________ or _______________ can be written as rational numbers. But
_______________ numbers cannot be written as fractions. Their decimal parts
neither repeat nor terminate. Below give two examples of this kind of decimal:
5. Use the “Special K Method” when necessary to fill in the blanks using <, > or =.
(a)
(b)
1
4
1
4
0.25
(c) 0.249
0.25
0.24 9
(d) 0.249
0.25
Decimal Conversion 3