Converting Fractions, Decimals

Converting Fractions, Decimals




Integers


Integers have no digits to the right of the decimal point. Examples of integers are 628, 3232542364357, and -54.
In the number 628,
8 stands for 8 ones2 stands for 2 tens6 stands for 6 hundreds
So 628 represents the sum of 6 hundreds, 2 tens, and 8 ones, or 600 + 20 + 8.

Base 10


When we write numbers, we use a system mathematicians call "base 10." In base 10, the first number to the left of the decimal point represents the number of 1's, the second number represents the number of 10's, the third number represents the number of 100's, the fourth number represents the number of 1000's, and so on.
Here are the place values:
Notice that as we move to the right, we divide by 10. We need to understand this to work with decimals.


Decimals


We have seen that to the left of the decimal place, the digits represent 1's, 10's, 100's, 1000's, and so on. To find the value of a decimal place, we divide the value of the decimal place to the left of it by 10.


Well, we do the same thing with digits to the right of the decimal place!
Let's look again at the sequence of numbers 1000, 100, 10, 1, and continue the pattern to get new terms by dividing previous terms by 10:
.1 = 1/10 .01 = 1/100.001 = 1/1000

So just as the digits to the left of the decimal represent 1's, 10's, 100's, and so forth, digits to the right of the decimal point represent 1/10's, 1/100's, 1/1000's, and so forth.



II. Changing a decimal to a fraction

Terminating Decimals

Now that we understand how decimal representation works, let's try to figure out the fractional equivalent of the decimal .345.
The 3 represents 3 tenths, the 4 represents 4 hundredths the 5 represents 5 thousandths
So, we can write .345 = 3/10 + 4/100 + 5/1000.
In order to add these fractions, we need to find the common denominator. In this case, it is 1000.


3/10 + 4/100 + 5/1000 = (300 + 40 + 5)/1000 = 345/1000.

The fraction 345/1000 needs some reducing. We can divide each side by 5: 345/1000 reduces to 69/200, so the final answer is:

.345 = 69/200.

Here's a shortcut for dealing with decimals: instead of writing out .345 = 3/10 + 4/100 + 5/1000, then finding the common denominator, adding, and reducing, just think:
.345 = 345/1000.

How about converting .7 or 47.6 to fractions?

.7 = 7/10 or seven tenths 47.6 = 476/10 or four hundred seventy-six tenths