Math 6H ( Periods 3, 6, & 7)

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 2 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 = 36/99 = .36363636...
we talked about the 1/7th family.