Transcript Convert Decimals to Fractions

Convert
Decimals to
Fractions
Focus 4 - Learning Goal #1: Students will know that there are numbers that
are not rational, and approximate them with rational numbers.
4
3
2
1
0
In addition to level
3.0 and above and
beyond what was
taught in class,
students may:
-Make connection
with other
concepts in math.
- Make
connection with
other content
areas.
Students will know
that there are
numbers that are not
rational, and
approximate them
with rational numbers.
- Convert a decimal
expansion that
repeats into a fraction.
- Approximate the
square root of a
number to the
hundredth & explain
the process.
- For all items listed as
a 2, students can
explain their process.
Students will know
the subset of real
numbers.
- Know that all
numbers have a
decimal expansion.
- Compare the size
of irrational
number.
- Locate
approximately
irrational numbers
on a number line.
With help from
the teacher, I
have partial
success with
level 2 and 3.
Even with help,
students have no
success with the
unit content.
Tens
Ones
.
Tenths
Hundredths
Thousandths
Ten Thousandths
Place Value Review
15 . 7456
What I already know…
0.5 = ½
0.75 = ¾
0.125 = 1/8
Use the place value of the last digit to determine the denominator.
Drop the decimal and use that number as the numerator.
• In the decimal 0.5 the “5” is in the tenths place so the
denominator will be “10.”
• The numerator will be 5. So the fraction is 5/10 which reduces to
½.
• In the decimal 0.75 the last digit is in the hundredths place so the
denominator will be “100.”
• The numerator will be 75. So the fraction is 75/100 which reduces
to ¾.
• In the decimal 0.125 the last digit is in the thousandths place so
the denominator will be “1000.”
• The numerator will be 125. So the fraction is 125/1000 which
reduces to 1/8.
Always
REDUCE
your
fractions!
Convert the following terminating
decimals to fractions.
1. 0.4
1. 4/10
2. Reduces to 2/5
2. 1.86
1. 1 and 86/100
2. Reduces to 1 43/50
3. 0.795
1. 795/1000
2. Reduces to 159/200
What about nonterminating decimals?
• How do you convert
0.1111111111….to a
fraction?
• We are told that repeating
decimals are rational
numbers.
• However, to be a rational
number it must be able to
be written as a fraction of
a/ .
b
Steps to change a non-terminating
decimal to a fraction:
 Convert 0.111111111… to a fraction
 How many digits are repeating?
 1 digit repeats
 Place the repeating digit over that many 9s.
 1/9
 Reduce, if possible.
 This means that the fraction 1/9
is equal to 0.111111…
 With your calculator, divide 1 by 9.
What do you get?
Try the steps again:
 Convert 0.135135135… to a fraction.
 How may digits are repeating?
 3 digits repeat.
 Place the repeating digits over that many 9s.

135/
999
 Reduce if possible.
 This means that the fraction 135/999 which
reduces to 5/37 is equal to 0.135135135…
 With your calculator, divide 135 by 999.
What do you get?
 Divide 5 by 37. What do you get?
One more time together:
 Convert 4.78787878… to a fraction.
 How many digits are repeating.
 2 digits repeat.
 Place the repeating digits over that many 9s.

78/
99
 Reduce if possible.
 Divide the numerator and denominator by 3.
 This means that the fraction 4 78/99 reduces to
4 26/33 is equal to 4.7878…
 With your calculator, divide 78 by 99.
What do you get?
 Divide 26 by 33. What do you get?
Your turn.
Change the following repeating
decimals to fractions.
1. 0.4444444…
1.
4/
9
2. 1.54545454….
1.
154/
54/
=
1
99
99
3. 0.36363636…
1.
36/
99
= 4/11