Percent - Northern Arizona University
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. Consider the fraction[pic]. The decimal representation of [pic] is 0.5 since[pic].
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 [pic].
Let n = [pic]. Thus 100n = [pic].
Then subtract the two equations: 100n = [pic]
– n = [pic]
___________
99n = 34
So… n = [pic].
Recall that n = [pic] as well. And so [pic]=[pic].
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) [pic]=__________________ (b) [pic]=__________________
(c) [pic]=__________________ (d) [pic]=__________________
(e) [pic]=__________________ (f) [pic]=__________________
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? |
|[pic] | | | |
|[pic] | | | |
|[pic] | | | |
|[pic] | | | |
|[pic] | | | |
|[pic] | | | |
Rule:_____________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
3. A student says that the fraction [pic]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 [pic]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) [pic] 0.25 (c) [pic] 0.25
(b) [pic] [pic] (d) 0.249 0.25
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