Rational Numbers: Convert Fractions to Decimals and Decimals to Fractions Review
CCSS Standard
Prerequisite for 8.NS.1
Materials: In-class worksheet: Writing Fractions as Decimals and Decimals as Fractions
Homework worksheet: Fraction/Decimal Review
Suggested Lesson Structure:
 Hand out worksheets
 Allow students to work independently on the worksheet for 10-15 minutes.
 Then, have students work in groups to discuss the worksheet and compare answers for
another 10-15 minutes.
 Finally, go over the answers and discuss problems where students encountered
difficulties.
Homework: Fraction/Decimal Review Worksheet
(Students will use the In-class worksheet as a guide - it is recommended to have
students keep the In-class worksheets in the notes section of their binder)
Reference Materials:
Holt McDougal Mathematics Grade 8: Ch 1-1: Holt McDougal Mathematics
Explorations in CORE MATH Grade 8 ISBN 978-0-547-64727-2
EXPLORATIONS 7 Chapter 1-1: Holt McDougal Mathematics Explorations in CORE
MATH Grade 7 ISBN 978-0-547-87653-5 (Student and Teacher Addition)
Videos/Interactives:
Student Video: 10 minutes
http://www.teachertube.com/viewVideo.php?video_id=199126
Teacher Video: 28 minutes
https://www.teachingchannel.org/videos/repeating-decimals-lesson-plan
Rational Numbers
Writing Fractions as Decimals and Decimals as Fractions
𝑎
Rational Number – is a number that can be written as a ratio in the form , where a and b are
𝑏
integers and b is not zero.
Writing Fractions as Decimals
3
4
0.7
4√ 3 . 0 0
−2 8
2
−
________
Remember that the fraction bar means “divided by.”
Divide the numerator by the demoninator.
Divide until the remainder is 1, adding zeros after the
decimal point in the dividend as needed.
3
= ____________
4
2
3
0.6
3√ 2 . 0 0
−
_______
−
________
−
________
2
3
= ____________
Will this division ever end in a remainder of 0?
Explain?
_________________________________________
Describe the quotient.
________________________________________
When a decimal has one or more digits that repeat indefinitely,
write the decimal with a bar over the repeating digit(s).
Write each fraction as a decimal.
1a.
6
11
_________________ 1b.
3
8
____________________
1c.
2
5
_____________________
2
Write 2 as a decimal. __________________
3
There are two types of decimals that are rational numbers:
Terminating Decimal – after the decimal point , there is a finite number of digits.
Repeating Decimal – after the decimal, there may be a block of one or more digits that are not all
���� is an example where 45 and are the repeating digits.
zero that repeat indefinitely. 0.645
Every rational number can be written as a terminating decimal or a repeating decimal.
Writing Decimals as Fractions
0.825
The decimal 0.825 means “825 thousandths.” Write this as a fraction.
Then simplify the fraction.
825 ÷
1000 ÷
0.825 =
Reflection:
=
40
How do you know that 0.825 𝑎𝑛𝑑 0. 3� can be written as fractions?
____________________________________
Write each decimal as a fraction.
� ____________________
1a. 0.12 _________________ 1b. 0. 3
1c. 1.4 _____________________
Name: _________________________
Fraction/Decimal Review (Homework)
1. Point P best represents what mixed number?
__________________
P
10
12
11
2. Order the numbers form least to greatest:
5
0, − , −3.5, −1
___________________
2
3. Place each of the numbers, as accurately as possible, on a number line. Label each with the letter next to the
expression.
𝑎) |−12|
𝑏) − 11
𝑐)
−32
3
𝑑)
23
−2
𝑒)
−57
−4
� as a common fraction in simplest terms.
4. Write 0. 3
___________________
5. Write 0.36 as a common fraction in simplest terms.
___________________
7
6. Write the decimal equivalent of .
___________________
8
1
1
7. An object on the moon weighs of it’s weight on the earth. Write as a fraction.
___________________
8. Round 28.25008 to the nearest tenth.
___________________
9. Round 7.47075 to the nearest thousandth.
___________________
6
6