Download Gr8 Topic 2 Convert Repeating Decimals

Name____________________________________________ Period____ Date________________________
8th Grade: Topic 2 REAL NUMBERS: Converting Repeating Decimals Into Fractions
OBJECTIVES:
 Convert fractions into decimals using division.
 Convert rational numbers in the form of repeating decimals into fractions.
EXPLORE: In the Overview, you reviewed rational numbers. Rational numbers can be written as decimals
that either terminate or repeat. To turn a terminating decimal into a fraction, convert the decimal to the sum
of two fractions and simplify.
Play the animation on Page 1 to see an example of this process.
Page 1: Convert 1.375 to an improper fraction
Page 2: Convert the following decimals into improper fractions and check your answer online.
a) 2.625
b) 3.78
c) 1.9375
Page 3 & Page 4: Converting a “repeating” decimal into a fraction.
Like terminating decimals, repeating decimals are rational numbers. And you know that all rational numbers
can be written as fractions. How would you write a repeating decimal such as 0.135 as a fraction?
On Page 4: Investigate some patterns. Divide the following fractions using a calculator.
What do you notice?
a.
e.
2
9
=
8
999
b.
=
What patterns did you notice?
f.
7
9
=
37
999
c.
=
4
99
g.
=
d.
627
999
=
61
99
=
Page 5: Write 0.135 as a fraction using the pattern you found for converting repeating decimals to fractions.
(The numbers 135 repeat every three digits, which means the denominator should have three digits, and
therefore be 999.)
Write the following repeating decimals as fractions. Use the pattern you found. Use a calculator to check
your answer.
a.
0.23
b . 0.054
c. 0.1
d. 2.65
Page 6:
Now, consider the repeating decimal 0.273. Can you use the pattern you discovered to
convert this rational number to a fraction? Why or why not?
In the patterns you have been exploring, the repeating sequence begins immediately after the decimal point.
But in this number, the sequence does not begin repeating until after the 2 in the tenths place, so the pattern
does not hold. Play the animation to see how to convert this type of repeating decimal to a fraction.
Take notes on the process!
Page 7:
a. 0.81 =
Check your understanding. Convert the repeating decimals to fractions.
b.
0.145 =
c.
0.562
Page 8: You may be wondering why the denominators 9, 99, 999, and, in some instances, 990 produce
repeating decimals. This interesting observation can be explained by writing and solving some simple
equations. Play the animation to use variables and equations to write 0.46 as a fraction. You will see why
the denominators 9, 99, and 999 produce repeating decimals. TAKE NOTES !
0.46 = 𝒙
Can you apply what you just learned to convert
0.581 to a fraction by writing and solving an
equation?
0.581
=
𝒙
Page 9: You used equations and variables to explain the pattern for converting a repeating decimal to a
fraction in cases like 0.581, where the denominator is 999.
But how do you explain that 0.273
=
271
990
?
This example does not quite follow the pattern of 9, 99, or 999 as the denominator.
Play the animation to explain this solution using equations and variables. TAKE NOTES !
0.273 = 𝒙
Practice Problems: Convert the following repeating decimals to fractions.
a. 0.4 =
b. 0.07 =
c. 2.21 =
d. 0.578 =
e. 1.381 =
f. 2.005 =