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 = 1.6 x 1.6 = ² = 1.7 x 1.7 = ² = 1.8 x 1.8 = 3.24

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

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 = 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

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

….. x = x = or 1000x = x = x 1000x – x = x – x therefore 999x = 234

Do You See the Pattern? Can you do this mentally yet? – What is the fractional equivalent of ….?

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

Exit Find the fractional equivalent: – 1) ….. – 2) …… – 3) …….