Writing Decimals as Fractions

1
Writing Decimals as Fractions
2
What is the fraction representation of each
decimal?
0.3
3/10
0.27
27/100
493/1000
0.493
3
REMINDER!!

• ALWAYS WRITE FRACTIONS IN SIMPLEST FORM.
• Example
• 0.45 45/100 9/20
• 2.6 2 6/10 2 3/5

4

• 0.3333.
• What is the fraction representation of this
  decimal?

5
0.454545..
How could you write this decimal as a fraction?
6
45/100 0.45

• Making the denominator greater does what to a
  fraction?

It makes the fraction smaller.
Make the denominator a bit greater.
45/101 0.44554455
You will discover that the fraction is even less.
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Todays problems will involve looking for
patterns to help write repeating decimals as
fractions.

• Assignment
• Complete handout 5.3
• Class discussion
• Complete Follow Up problems 5.3

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SUMMARY

• What is the decimal representation for these
  fractions?

19/9 20/9
2.11111
2.22222
9

• What is the decimal representation for these
  fractions?

50/99 100/99
0.505050


1.010101
10
What fraction is equivalent to
4.111111 0.353535
Answers 4 1/9 or 37/9
35/99
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Can you predict the decimal representations for
fractions with denominators of 999 and 9999?
If there are 3 digits repeating the denominator
will be 3 nines. If there are 4 digits repeating
the denominator will be 4 nines.
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Exploration
Another method to change repeating decimals to
fractions.
Change 0.454545 to a fraction Call the unknown
fraction N. N 0.454545.. Multiply
both sides of the equation by 100. 100N
45.454545 Subtract the first equation from the
second 100N 45.454545 - N
0.454545 99N 45 Therefore N 45/99
or 5/11