Estimating Square Roots to the Tenths and Hundredths Place

Review

• Yesterday we discussed estimating square roots between two integers and discussed how to improve our estimate to the tenths place.

• Estimate the square root of 3

• 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

• 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

• Where would you place , , and ?

– Would you estimate the to be more or less than 2.5?

• Estimate to the tenths place.

• Estimate the to the tenths place

Think Pair Share

• Estimate to the tenths place

Discussion

• How could we improve the estimate to the hundredths place?

Converting Repeating Decimals to Fractions

This Gets a Little Complex

• As we go through a few examples, I want you to look for patterns.

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

What About This

0.0034

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

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 =

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 =

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 =

Do You See the Pattern?

• Can you do this mentally yet?

– What is the fractional equivalent of 0.434343….?

• Why might it be important to be able to convert a repeating decimal to a fraction?

Exit

• Find the fractional equivalent:

– 1) 0.77777…..

– 2) 0.527527……

– 3) 0.91269126…….