Class Discussion
• Who can explain what a
fraction is?
• Who can explain what a
decimal is?
• Can you find a decimal
that is equivalent to ¼?
• What method did you use
to find this?
Converting Fractions to Decimals
• To convert a Fraction to a Decimal without a calculator,
follow these steps:
• Step 1: Find a number you can multiply by the bottom of
the fraction to make it 10, or 100, or 1000, or any 1
followed by 0s.
• Step 2: Multiply both top and bottom by that number.
• Step 3. Then write down just the top number, putting the
decimal place in the correct spot (one space from the right
for every zero in the bottom number)
Method #1: Converting with Proportions
• Example # 1: Express 3/4 as a Decimal
• Step 1: We can multiply 4 by 25 to become
100
• Step 2: Multiply top and bottom by 25
3 = 75
4
100
Example # 1 continued….
• Step 3: Write down 75 with the decimal place
2 spaces from the right (because 100 has 2
zeros);
• Answer = 0.75
• Can you explain what we just did?
• Try to express ¼ as a decimal using method #
1.
Method #2: Convert by Dividing
 Example #1: to write 5/8 as a decimal, we need
to calculate 5 ÷ 8:
0.625
8 √ 5.000
So = 0.625 as a decimal.
 Try this example: write 4/5 as a decimal using
division (method #2).
Compare and Order Rational Numbers
** REMEMBER! A decimal like 1.6666…. is called a
repeating decimal because it does not terminate
but has a 6 that repeats.
Use bar notation to write repeating decimals.
Place the bar only over the digits that repeat.
1.666...  1.6
When repeating decimals occur in real-life situations,
they are usually rounded to a certain place value.
Compare and Order Rational Numbers
1. Give an example of a repeating decimal where two
digits repeat. Explain why your number is a rational
number.
2. Write 5.321321321… using bar notation.
3. Identify the fraction that cannot be expressed as the
same type of decimal as the other three fractions.
1
Explain why.4
1
1
11
2
9
3
Comparing and Ordering Rational Numbers
Order the numbers from least to greatest.
4 , 0.93, and 0.9
5
Write as decimals with the same number of places.
4 = 0.80
5
0.93 = 0.93
0.9 = 0.90
Graph the numbers on a number line.
0.93
0
0.2
0.4
0.6
0.8
1
Comparing and Ordering Rational Numbers
Order the numbers from least to greatest.
4 , 0.93, and 0.9
5
The values on a number line increase as we
move from left to right.
0.80 < 0.90 < 0.93
Place the decimals in order.
4 , 0.9, 0.93
5
0.93
0
0.2
0.4
0.6
0.8
1
Comparing and Ordering Rational Numbers
Order the numbers from least to greatest.
3 , 0.84, and 0.7
5
Write as decimals with the same number of places.
3 = 0.60
5
0.84 = 0.84
0.7 = 0.70
Graph the numbers on a number line.
0.84
0
0.2
0.4
0.6
0.8
1
Comparing and Ordering Rational Numbers
Order the numbers from least to greatest.
3 , 0.84, and 0.7
5
The values on a number line increase as we
move from left to right.
0.60 < 0.70 < 0.84
Place the decimals in order.
3 , 0.7, 0.84
5
0.84
0
0.2
0.4
0.6
0.8
1
Comparing and Ordering Rational Numbers
Extra Practice
Choose the greater number.
3
3 or 4
2. 5 or 2
1.
8
7
7
10
3
2
3
Place the numbers in order from least to greatest
3. 0.3, 0.32, 0.312
0.3, 0.312, 0.32
4. 5 , 0.8, 0.826
6
0.8, 0.826, 5
6
Real World Example
The table shows the portion of some
common materials and products that
are recycled.
Do we recycle more or less than half of
the paper we produce? Explain.
Less, 5 is less than half of 11 or 5.5
Material
Fraction
Recycled
Paper
5
11
Aluminum
Cans
Glass
5
8
2
5
Scrap
Tires
3
4
Do we recycle more or less than half of the aluminum
cans? Explain.
More, 5 is greater than half of 8 or 4
Comparing and Ordering Rational Numbers
Word Problem
Jose’s cross-country team is getting ready for
a big meet. On Monday they ran 3.7 miles, on
Tuesday they ran 3 3 miles, and on Wednesday
8
they ran 11 miles.
4
On which day did they run the greatest
distance?
Monday
Comparing and Ordering Rational Numbers
Word Problem #2
As of the All-Star Baseball 2011 game, which
Arizona Diamondback player had the better
batting average, Stephen Drew with a .259
batting average or Chris Young with a batting
131 average?
500
Chris Young .262 batting average
Compare and Order Rational Numbers
What if a baseball pitcher won 6 out of 11 games he
started. To find his winning average to the nearest
thousandth place you would divide 6 by 11:
6
11
6
11
=
=
0.545454…
Look to the ten thousandth
place. 4< 5
0.545
0.545 is the pitcher’s winning average.
Use the rounding
rules, so the 5 in the
thousandths place
stays the same
Skittles Activity
1. Sort your skittles into groups by color.
2. Find the fraction of each color.
3. Convert your fractions into a decimals.
4. Record your data on chart paper.
5. Compare your results with your group members.
6. Answer the remaining questions on the worksheet.