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Estimating Square Roots to the Tenths and Hundredths Place
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Review
• Yesterday we discussed estimating square roots between two integers and discussed how to improve our estimate to the tenths place.
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• Estimate the square root of 3
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• At this point, we have to make an educated guess and calculate the squares of rational numbers which include decimals
– You should notice that the square root of 3 is most likely larger than 1.5
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• 1.5² = 1.5 x 1.5 = 2.25
• 1.6² = 1.6 x 1.6 = 2.56
• 1.7² = 1.7 x 1.7 = 2.89
• 1.8² = 1.8 x 1.8 = 3.24
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• Where would you place , , and ?
– Would you estimate the to be more or less than 2.5?
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• Estimate to the tenths place.
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• Estimate the to the tenths place
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Think Pair Share
• Estimate to the tenths place
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Discussion
• How could we improve the estimate to the hundredths place?
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Converting Repeating Decimals to Fractions
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This Gets a Little Complex
• As we go through a few examples, I want you to look for patterns.
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Multiplying by a power of 10
• What happens to my decimal any number every time I multiply by ten?
– Start with the number 8.0
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What About This
0.0034
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Repeating Decimals
• We need to get the entire portion of the decimal that repeats to the left side of the decimal place
• To do this we will multiply each side by a power of ten until this is accomplished
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Repeating Decimals• Lets look at 0.4• We will make x = 0.4
• If I multiply both sides by 10 I get: 10x = 4.4 which can break into 10x = 4 + 0.4 x = 0.4 so I can substitute 10x = 4 + (x)
• Now I need to get one of the variables isolated• 10x – x = 4 + x – x therefore 9x = 4
x =
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0.818181…….
• Let x = 0.81
• 100x = 81.81 or 100x = 81 + 0.81
• 100x = 81 + x
• 100x – x = 81 + x – x therefore 99x = 81
x =
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0.234234234…..
x = 0.234
1000x = 234.234 or 1000x = 234 + 0.234
1000x = 234 + x
1000x – x = 234 + x – x therefore 999x = 234
x =
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Do You See the Pattern?
• Can you do this mentally yet?
– What is the fractional equivalent of 0.434343….?
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• Why might it be important to be able to convert a repeating decimal to a fraction?
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Exit
• Find the fractional equivalent:
– 1) 0.77777…..
– 2) 0.527527……
– 3) 0.91269126…….