Problem of the Day

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Problem of the Day

• How many triangles are in the figure?

2
Representing Fractions as Decimals
3
Can you find a decimal that is equivalent to this
fraction?

• 1/4

0.25
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What decimal is equivalent to 1/8?
0.125
5
Find a decimal equivalent to 1/3?

• 0.33333333

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Can you find a decimal that is equivalent to this
fraction?

• 1/11

0.09090909
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1/4 and 1/8 have decimals that end. Decimals
like these are called terminating decimals.
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1/3 and 1/11 have decimals with groups of digits
that repeat forever. Decimals like these are
called repeating decimals.
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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

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Problem 5.2 Follow-Up

• Find three fractions with the same decimal
  representation as the given fraction.
• 2/5
• 5/6

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

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Without using a calculator, write the fraction
4/33 as a decimal.

• Does the decimal terminate or repeat?

What is the repeating part?
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Without dividing, do you think that you can
predict whether a fraction has a repeating or
terminating decimal representation?
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Ex. 1/8 125/1000 125/2x2x2x5x5x50.125

• 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.

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ACE Problems 1-421-24