Converting Fractions to Decimals and Order
of Operations
- Converting Fractions to Decimals
To convert fractions to decimals we just divide. The only catch is
when should we stop. Sometimes we end when there is no remainder.
Example
Convert the fraction 3/8 to a decimal.
Solution
0.375
8 |
3.000
24
60
56
40
40
0
Hence
3
=
0.375
8
Other times the digit repeats itself
Example
Convert the fraction 5/6 to a decimal.
Solution
0.833
6 |
5.000
48
20
18
20
18
20
We see that if we keep working it out we will continually get
3. That is
5
=
0.833333...
6
We put a bar over the 3 to indicate that the 3 repeats.
0.83333... = 0.83
Example
Convert the fraction 4 2/7 to a decimal.
Solution
Divide only the fractional part
0.285714
7 |
2.00000000
14
60
56
40
35
50
49
10
7
30
28
20 We
are back to where we began.
Hence
2
4
= .285714Notice the 4 from the mixed number is the whole
number part.
7
Example
Fill in the green blank with "<" , ">", or
"="
2
0.133
15
Solution
We first convert the fraction into a decimal. Then
compare. We will need to divide until we recognize a difference or
recognize equality
0.13
15 |
2.00
15
50
45
50
We see that this is the repeating decimal
0.13
= 0.133333...
Now notice that
0.133 = 0.133000000... <
0.1333333...
Exercises
Convert the following fractions to decimals
- 3/4
- 8 5/9
- 7 2/11
- Order of Operations
Just as with whole numbers and fractions the order of operations is:
- Inside parentheses
- Exponents
- Multiplication and Division For
a tie go left first
- Addition and Subtraction
For a tie go left first
Example
Calculate
(2.1 - 1)2
+ 5.6 x 4
Solution
(2.1 - 1)2
+ 5.6 x 4
= (1.1)2
+ 5.6 x 4
= 1.21
+ 5.6 x 4 (1.1)2
= 1.1 x 1.1 = 1.21
=
1.21 + 22.4
5.6 x 4 = 22.4
= 23.61
Exercise
Calculate
(5 -
2.3) ÷ 0.12 + 3.2 x 0.5
- Application
Your drill bit is 3/16 inches in radius, but the screw that is to go
into the hole is supposed to be 0.2 inches in radius. How much bigger
is the screw then the hole?
Solution
We convert 3/16 to a decimal.
0.1875
16 |
3.0000
16
140
128
120
112
80
80
0
Finding how much bigger is a subtraction problem
199
0.20010
- 0.1875
0.0125
The radius of the screw is 0.0125 inches bigger than the radius of
the hole.
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