ࡱ> ,.+r` bjbj 4D ,88Ll02  2 2 2 I"I"I"}0000000$02h40<#!|I"<#<#02 2 0z%z%z%<#X2 2 }0z%<#}0z%z%r .T.2  @>#].1/L000k.z<5d$<5.<5.LI">",z%"$"eI"I"I"00 %pI"I"I"0<#<#<#<#d\\ 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 EMBED Equation.3 . The decimal representation of  EMBED Equation.3  is 0.5 since EMBED Equation.3 . 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  EMBED Equation.3 . Let n =  EMBED Equation.3 . Thus 100n =  EMBED Equation.3 . Then subtract the two equations: 100n =  EMBED Equation.3  n =  EMBED Equation.3  ___________ 99n = 34 So n =  EMBED Equation.3 . Recall that n =  EMBED Equation.3  as well. And so  EMBED Equation.3 = EMBED Equation.3 . Decimal Conversion 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)  EMBED Equation.3 =__________________ (b)  EMBED Equation.3 =__________________ (c)  EMBED Equation.3 =__________________ (d)  EMBED Equation.3 =__________________ (e)  EMBED Equation.3 =__________________ (f)  EMBED Equation.3 =__________________ 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. FractionReduced FractionPrime Factorization of DenominatorTerminate or Repeat? EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  Rule:_____________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ A student says that the fraction  EMBED Equation.3 should be a repeating decimal because the factors of the denominator include a 3 as well as 2s and 5s. But on her calculator  EMBED Equation.3 seems to terminate. How would you explain this? 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: Use the Special K Method when necessary to fill in the blanks using <, > or =. 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