# Thread: Converting fractions to decimals--without a calculator

1. ## Converting fractions to decimals--without a calculator

I have a test tomorrow, and was given examples of the types of problems that I'd be taking. I figured everything out, except this one.

A student misses 5 of her 31 classes in a semester. What is her attendance percentage?
26/31 x 100 = __%

This seems ridiculously easy, but during the test, calculators are forbidden. So I can't just type in 26/31 and be done. I looked up methods to manually convert fractions to decimals, but the only one I found works like this:

Say I'm converting 3/4. I need to find a way to make the denominator (4) into a number divisible by 10. In this case, that would mean multiply by 25. Now I multiply 3/4 by 25/25, and get 75/100. Therefore, .75 would be the decimal form.

This works fine...but only for certain numbers. 31? I got to the billions trying to find a working number, and got nothing. Considering that the test is timed, and I don't want to have to manually check 10-100-1000-10000-100000-1000000-10000000 etc. etc. etc. for whatever denominator I get. So...is there another way? Or am I stuck with the 10-divisible number theorem?

Help is appreciated

2. Originally Posted by Nightfire
So...is there another way? Or am I stuck with the 10-divisible number theorem?

Help is appreciated
You should just use long division. When you run out of digits to "bring down," just tack zeros onto the end of the dividend.

3. Originally Posted by Nightfire
A student misses 5 of her 31 classes in a semester. What is her attendance percentage?
26/31 x 100 = __%

This seems ridiculously easy, but during the test, calculators are forbidden. So I can't just type in 26/31 and be done....
They'll need to tell you what sort of answer they're wanting. If you need to give the percentage to, say, one decimal place, then go one place further in the long division:

[HTML]long division:

.8387
--------
31 )26.0000
248
--------
120
93
--------
270
248
--------
220
217
-------
3[/HTML]
Since the "7" will cause you to round up, the answer would be "83.9%".

On the other hand, if they want a "mixed number" sort of percentage, then stop at one extra digit (the first two being the whole-number part of the percent), and then tack on the remainder-over-divisor fractional part:

[HTML]long division:

.83
------
31 )26.00
248
------
120
93
------
27[/HTML]
So the answer would be $\displaystyle \mbox{"}83\frac{27}{31}\%\mbox{"}$.