i dont knw how to write the decimals as comon fractoins in simplest form?

[coolj999]

:conf used::icon_c rying::icon _crying:

[MAS1]

Originally Posted by coolj999

:conf used::icon_c rying::icon _crying:

Here are a couple of examples for terminating decimals:

1. 0.465
Look at a non-zero digit which is in the smallest place. In this case it is the 5 in the thousandths place. This means the denominator for your fraction will be 1000. Now write the digits "465" in the numerator. You should have:
465/1000 which is four hundred sixty five thousandths.
Now see if you can simplify the fraction. 5 is a factor of both the numerator and denominator so divide both by 5 giving
93/200

2. 2.76
Ignore the whole number part for now.
0.76 = 76/100 = 38/50 = 19/25
Now add the whole number part back in creating the mixed number 2 19/25

To find the fraction for non-terminating, repeating decimals:

1. 0.33333...
Let x = 3.33333...
then 10x = 3.33333...
10x - x = 3.3333... - 0.3333...
9x = 3 (All of the 3's to the right of the decimal place cancel out)
x = 3/9 = 1/3

2. 0.166666...
Let x = 0.166666...
10x = 1.66666...
10x - x = 1.66666... - 0.1666666...
9x = 1.5
18x = 3
x = 3/18 = 1/6

3. 0.142857142857142857...
x = 0.142857142857142857...
1000000x = 142857.142857142857142857...
1000000x - x = 142857
999999x = 142857
x = 142857/999999 = 15873/111111 = 5291/37037 = 1/7

Hope this helps!

[Mr. Hui]

I wonder what happens when you try to simplify 0.999... ?

[meetballs]

1/7 is the Answer

[MAS1]

Originally Posted by meetballs

1/7 is the Answer

Ummm, no.

[Lisasmith111]

Originally Posted by Mr. Hui

I wonder what happens when you try to simplify 0.999... ?

Mr Hui,
I guess using the above method we would have

x= 0.9999; 10x = 9.9999

so 10x - x = 9.9999 - 0.9999

then 9x = 9

so x = 1

0.9999... is as near to 1 as makes no odds

What do you think?

Lisa Smith

[Mr. Hui]

Thanks for typing it out, Lisa.

The fact that 0.999... is so close to 1, and the difference between 0.999... and 1 is infinitesimally small, "proves" that 0.999... = 1.

[tiger190]

Originally Posted by Mr. Hui

Thanks for typing it out, Lisa.

The fact that 0.999... is so close to 1, and the difference between 0.999... and 1 is infinitesimally small, "proves" that 0.999... = 1.

i agree wit u

[Lisasmith111]

Originally Posted by Mr. Hui

I wonder what happens when you try to simplify 0.999... ?

Mr Hui,

I think this one becomes 1 as the following illustrates:-

let x = 0.999 and 10x = 9.999

10x - x = 9
9x = 9
x = 1

0.999 is approx = 1 (I guess there has to be some rounding at due to the nature of decimals, whereas fractions can be more exact.

[MAS1]

Originally Posted by Lisasmith111

Mr Hui,

I think this one becomes 1 as the following illustrates:-

let x = 0.999 and 10x = 9.999

10x - x = 9
9x = 9
x = 1

0.999 is approx = 1 (I guess there has to be some rounding at due to the nature of decimals, whereas fractions can be more exact.

Lisa, there is no rounding involved. 0.999999999... is exactly equal to 1 by the reasoning you showed. If x = 0.99999999... and 10x = 9.999999... then when you subtract x from 10x, it cancels out all of the 9's to the right of the decimal point.
10 - x = 9.999999... - 0.99999999...
9x = 9
x = 1
Substituting back gives 1 = 0.99999...