3.5Converting Fraction to Decimals and the Order of Operations (234)
Objectives:
Convert a fraction to a decimal
Use the order of operations with decimals
3.5 Converting a Fraction to a Decimal (234)
Every decimal in this chapter can be expressed as an equivalent fraction, and vice versa.
Converting a fraction to an equivalent decimal (234)
Divide the denominator into the numerator until
The remainder becomes zero, or
The remainder repeats itself, or
The desired number of decimal places in achieved
Examples: 1/8 0.1255/3 1.666 = 1.6 2/27 to 2 decimals 0.074
8 ) 1.0003 ) 5.00027 ) 2.000
1 89
110
108
3
TerminatingRepeatingRepeating
PP1 Write as an equivalent decimal (235)
0.3125 0.1375
a) 5/1616 ) 5.0000b)80 ) 11.0000
4 8 8 0
20 3 00
16 2 40
40 600
32 560
80 400
80 400
If you end up with a zero remainder, you have a terminating decimal. Otherwise, you will get a group of digits that repeats forever more, then you have a repeating zero. This is true for all rational numbers. Irrational numbers like the square root of 2 is another story.
PP2 Write as an equivalent fraction (236)
0.636 0.63 0.533 0.53 0.2954 0.2954
a)7/11 11 ) 7.000b) 8/15 15 ) 8.00000c) 13/44 44 ) 13.0000
6 6 7 5 8 8
40 50 4 20
33 45 3 96
70 50 240
66 45 220
40 repeating 50 repeating 200
176
repeating 24
Note: What about mixed numbers
12 1/2 1/2 = 0.512 1/2 = 12.5
Do the fraction, thenjust put the whole portion in front of the decimal
PP3 Write as an equivalent decimal (236)
0.612.61 1.0370 1.037
a) 2 11/18 18 ) 11.0000b) 28/27 27 ) 28.00000
10 8 27
20 1 00
18 81
20 repeating 190
189
100 repeating
PP4 Express 19/24 as a decimal rounded to the nearest thousandth (237)
0.7916 0.792
24 ) 19.0000
16 8
2 20
2 16
40
24
160
144
16
Remember the order of decimals is determined by matching digits from left to right
1.63451.63451
PP5 Essentially, determine which of the following { < , > , = } fits between the given digits. (238)
5/8 _____ 0.63 0.625
0.625 < 0.638 ) 5.000
3.6.1 Using the Order of Operations
The priority of the operations still haven’t changed and probably never will.
PP6Evaluate 0.3 × 0.5 + (0.4)3 - 0.036
0.3 × 0.5 + 0.064 - 0.036
0.15 + 0.064 - 0.036
0.214 - 0.036
0.178
PP7Evaluate 6.56 ÷ ( 2 – 0.36 ) + ( 8.5 – 8.3 )2
6.56 ÷ ( 1.64 ) + ( 8.5 - 8.3 )2
6.56 ÷ ( 1.64 ) + ( 0.2 )2 4.0
6.56 ÷ ( 1.64 ) + 0.041.64 ) 6.56 0
4.0 + 0.04 6 56
4.04
Developing your study skills
We live in a very technical world, and you can’t afford to quit learning your math skills. It does take time and effort. You will find that regular study and daily practice are required.