In the last section, we learned how to convert some special Base 10 fractions into decimals, and vice versa.
Now, were going to learn how to convert ANY fraction into a decimal.
And it turns out to be really simple… all you have to do is divide.
Since a fraction is really just a division problem, if you go ahead and DO the division,
you’ll get an answer, and that answer will be the decimal value of the fraction.
Now there’s two ways we can do the division …the easy way, and the hard way.
Now just because I’m mean, we’re going to start with the hard way.
Let’s take the fraction one-half and convert it into a regular division problem with this division symbol.
Now, all we have to do is follow the procedure for division.
We just see how many times this ‘2’ divides into this ‘1’.
Uh Oh! It won’t divide any times. ‘2’ is bigger than ‘1’.
…looks like we’re going to need some help, and that’s where the decimal point comes in.
Now you remember that in the last section, we learned that ‘1’ could be written as 1.0 or 1.00 or 1.000 and its value is still ‘1’.
Let’s try doing that here and see what happens.
After the ‘1’, put a decimal point and then a zero in the tenths place.
Now our division problem looks like 10 divided by 2, and that’s easy to do!
The only difference is we have a decimal point.
Let’s ignore the decimal point for a minute and pretend that our problem really is 10 divided by 2.
So 2 will go into 10 five times because 5 times 2 equals 10, and that leaves no remainder. So we’re done, right?
Not so fast, we’ve got that decimal point to deal with.
And we know that 5 can’t be the answer because 5 is bigger than one-half.
We just need to include the decimal point in our answer for it to be correct.
We put it directly above the decimal point in our problem.
There… now our answer is “point 5” (or 0.5 which is the more proper way to write it.)
So, by dividing, we figured out that the decimal value of 1/2 is 0.5
Now let’s try converting the fraction 3/4 by dividing.
Of course we start by rewriting our fraction like this: 3 divided by 4.
And again, we run into the same problem: 4 is too big to go into 3,
so it looks like we’re going to need a decimal point here too.
Let’s put a decimal point after the 3, and a zero in the tenths place to make 3.0
Now our problem almost looks like 30 divided by 4. Now if you remember your multiplication table,
you’ll know that 4 goes into 30 seven times because 7 times 4 is 28.
30 minus 28 leaves a remainder of 2, but we don’t want a remainder, so let’s keep going.
4 is too big to divide into 2, so the only way we can get rid of the remainder
is to use another zero in the hundredths place which make the number we’re dividing up kind of look like 300.
Now we can bring down that extra zero to make the remainder look like 20.
And 4 will go into 20 five times because 5 times 4 equals 20, and that leaves no remainder. Oh yeah!
But don’t forget, we need to include the decimal point in our answer.
Now if you’ve kept your column lined up like I have, you’ll see that the decimal point goes right here,
and that makes our answer: 0.75 So the decimal value of 3/4 is 0.75
Alright, let’s convert one more the hard way.
Let’s find the decimal value of 1/3 by dividing 1 by 3.
Again, 3 is too big to divide into 1, so we’ll need to use
a decimal point and another zero which makes our problem look like 10 divided by 3.
That’s easy! 3 goes into 10 three times because 3 times 3 equals 9. And that leaves a remainder of 1.
Just like before, we don’t want a remainder, so let’s use another zero so we can keep on dividing.
And that gives us 10 divided by 3 again.
Well, we know that 3 goes into 10 three times, and leave a remainder of 1.
Huh?! …still a remainder of 1. Well it looks like we’re gonna need another zero.
But that’s just gonna give us 10 divided by 3 again, which is going to give us another remainder of 1.
This looks like it might keep on going forever!
Some fractions are like that.
If you divide them, you’ll see a repeating pattern of numbers that continues on forever.
So the decimal value of 1/3 is 0.3333333…. and ‘3’s that keep on going forever!
But since we can’t keep writing ‘3’s forever, we can just stop and round the number off.
Or we can use this special symbol that means “this number repeats forever”.
Alright, so all we have to do to convert a fraction into a decimal is divide.
And so far, we’ve been doing that the hard way. But now, we’re gonna do it the easy way.
We’re gonna use a calculator!
Let’s try a couple with the calculator and see what we get.
To convert one-fourth, we just punch in 1 divided by 4 and we get 0.25
To convert two-thirds, we just punch in 2 divided by 3 and we get... “zero point a whole lot of sixes”.
…looks like we have another one of those repeating decimals.
Yep, this way is certainly is easier, and quicker too.
But it’s important to know how to do it both ways.
The five fractions that we’ve just converted are so common that it’s a good idea to memorize their decimal values.
Here there are again so you can review them:
1/4 = 0.25
1/3 = 0.33333…
1/2 = 0.5
2/3 = 0.66666…
and 3/4 = 0.75
So that’s how you convert any fraction into a decimal. You just divide!
And we already learned how you go the other way (to convert a decimal into a fraction) in the last section,
so be sure to review it if you need too.
In the next section, we’re going to learn a few tricks that we can use to help us compare the values of fractions,
but before that, …a quick review.
To convert ANY fraction to a decimal number, all you have to do is divide the top number by the bottom number.
Usually when you divide a fraction, you’ll need to do decimal division.
By using the decimal point, you can keep writing zeros in the decimal number places and continue dividing until you have no remainder.
Sometimes decimal division results in a pattern that keeps repeating forever.
When that happens, you can draw a line over the repeating digits instead of writing them forever.
Once you know how to do decimal division, I recommended that you convert fractions using a calculator since it’s quicker and easier.
And as always, be sure to do the exercises.
And don’t forget to practice dividing the hard way too,
because if you’re ever stranded on a deserted island without a calculator, you need to be able to do your math homework! ;-)
Learn more at www.mathantics.com