Estimating Square Roots to the Tenths and Hundredths

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

Think Pair Share •

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: 10 x = 4. 4 which can break into 10 x = 4 + 0. 4 x = 0. 4 so I can substitute 10 x = 4 + (x) • Now I need to get one of the variables isolated • 10 x – x = 4 + x – x therefore 9 x = 4

0. 818181……. • Let x = 0. 81 • 100 x = 81. 81 or 100 x = 81 + 0. 81 • 100 x = 81 + x • 100 x – x = 81 + x – x therefore 99 x = 81

0. 234234234…. . x = 0. 234 1000 x = 234 or 1000 x = 234 + 0. 234 1000 x = 234 + x 1000 x – x = 234 + x – x therefore 999 x = 234

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. 9126…….