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L09_filled - Day 09 Extended Expansions(Decimation with...

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1 Day 09 Extended Expansions (Decimation with Decimals) 2 Today’s Travel Plans Extended Decimal Expansions The Decimating Decimals Converting Fractions to Decimals …Doing it Long Division Style Lessons to be Learned Repetition, Repetition
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2 3 Extended Decimal Expansion We have seen that any integer has a decimal expansion since our number system is a Base-10 system , Recall from before that… Can we extend this this process to fractions so that a fraction may be written on a single line? 4 Extended Decimal Expansion II Consider the fraction which is equivalent to The second form, as we’ll see, is more convenient since the denominator is a power of 10 The numerator is an ___________ so it can be expanded in the usual way as follows…
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3 5 Extended Decimal Expansion III Thus we have Notice that just like an ____________ the fraction can be written a sum of products featuring a ________ digit number times a power of ______. Some of the 10’s have _______ number powers, just like a regular decimal expansion but… Some of the 10’s have __________ powers, which is _____ like a regular decimal expansion. 6 Extended Decimal Expansion VI Using this expansion we can write the fraction as the number The dot between 8 and 7 is known as a ____________ ________
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