Math 6A (Periods 2 & 4)

Changing a Fraction to a Decimal 6-5
There are two methods that can be used to change a fraction to a decimal.

1) find an equivalent fraction whose denominator is a power of 10. (this method does not always work but when it does it becomes really easy to change to a decimal)

13/25 multiply the numerator and the denominator by 4 to get 52/100 and then just close your eyes and see Chapter 3... and 0.52


2) divide the numerator by the denominator. It's a great way to determine your score out of 100 and then figure out your percent.

If you got 67/75 on the last test

divide 67 by 75 carefully 0.8933333... you earned a B+

take 3/8 and divide 3 by 8 8 goes into 3 0.375 times

so 3/8 = 0.375

If the numerator is smaller than the denominator we know our number must be between 0 and 1--> it must be a decimal.


When the remainder is 0 as in the case of dividing 3 by 8, it is called a terminating decimal.


By examining a fraction in lowest terms, we can determine whether the fraction can be expressed as a terminating decimal.

If the denominator has no prime factors other than 2 or 5, the decimal representation will terminate.

7/40

looking at 40 we notice the prime factorization ( oh no, it's Chapter 5)
40 = 2³·5 Since the only prime factors are 2 and 5

7/40 must terminate.

What about 5/12 ?

12 = 2²· 3 Since 3 is a prime factor of the denominator, the fraction cannot be expressed as a terminating decimal.


What about 9/12 ? At first it looks the same as the one above, but look carefully and realize 9/ 12 = 3/4

Since 4 = 2² , 4 has no other prime factors except 2, this can be expressed as a terminating decimal.


Let's look at 15/22
Since 22 has the prime factor of 11 we know that this will not terminate. In fact when you divide 15 by 22 you end up with 0.681818181...


We write this as ( Please check page 196) Notice that the bar is only over the 81 and represents a block  numbers that continues to repeat indefinitely and is called a repeating decimal.


EVERY FRACTION CAN BE EXPRESSED AS EITHER A TERMINATING DECIMAL OR A REPEATING DECIMAL.


Let's look at 4/9 = 0.4444444....

5/9 =

7/9 =


31/99 = 0.3131313131...

8/ 11 = 72/99 = .72727272...