How many triangles are in the figure? Problem of the Day How many triangles are in the figure?

Representing Fractions as Decimals

Can you find a decimal that is equivalent to this fraction? 1/4 0.25

What decimal is equivalent to 1/8? 0.125

Find a decimal equivalent to 1/3? 0.33333333… The three dots indicate that the pattern continues infinitely.

Can you find a decimal that is equivalent to this fraction? 1/11 How did you find these decimals? Did you notice any differences/similarities in these problems? 0.09090909…

1/4 and 1/8 have decimals that end 1/4 and 1/8 have decimals that end. Decimals like these are called terminating decimals.

1/3 and 1/11 have decimals with groups of digits that repeat forever 1/3 and 1/11 have decimals with groups of digits that repeat forever. Decimals like these are called repeating decimals. Students may think that these decimals terminate (because they end on the calculator). If you actually divide this out we clearly see that it goes on forever (infinite). We use a bar over the digits that repeat to indicate that they do repeat.

Problem 5.2 Write each fraction as a decimal, and tell whether the decimal is terminating or repeating. If the decimal is repeating, tell which digits repeat. 2/5 3/8 5/6 35/10 8/99 Do you see the repeating part of the decimal in the calculator display? Try converting at least one of these fractions without using a calculator to verify that the decimal does repeat.

Problem 5.2 Follow-Up Find three fractions with the same decimal representation as the given fraction. 2/5 5/6

Find a fraction that is equivalent to the given terminating decimal. 0.35 89.050

Without using a calculator, write the fraction 4/33 as a decimal. Does the decimal terminate or repeat? What is the repeating part?

Without dividing, do you think that you can predict whether a fraction has a repeating or terminating decimal representation?

For a fraction to terminate, it must be possible to express it as an equivalent fraction with a denominator of a power of 10 (10, 100, 1000, etc) This will happen if the fraction has only 2s and 5s as factors of its denominator. Ex. 1/8 = 125/1000 = 125/2x2x2x5x5x5=0.125

ACE Problems 1-4 21-24