Are you confused?
Numbers such as 4,580,103.7864892022 can be hard to read, especially when you see them on a calcula-
tor display that does not insert the commas. You can insert spaces on either side of the point, and also after
every third digit to the right of the decimal point. Those spaces will make the whole thing easier to read.
The above numeral would then look like this:
4,580,103. 786 489 202 2
Be careful when you insert spaces into a numeral! In this example, the lonely digit 2 at the end might
confuse some people. Also, note that the spaces between these digits don’t correspond to the places you’d
put the commas if you were to express them as a fraction. (You’ll see this in the “challenge” example
below.)
Here’s a challenge!
Break down 4,580,103.7864892022 into a sum of a single integer and a single fraction.
Solution
Let’s look to the left of the point first. The string of numbers is one big integer:
4,580,103
Now let’s look to the right of the point. There are 10 digits here. That means the denominator of the frac-
tion should be denoted as 1 with 10 ciphers after it, producing the fraction
7,864,892,022 / 10,000,000,000
The entire number is the sum of these:
4,580,103+ 7,864,892,022 / 10,000,000,000
Endless Decimals
Whenever you write out a decimal expression in the “real world,” it’s always a terminating
decimal. But in theory, the digits to the right of the decimal point can continue forever, so
you can never reach a spot where every digit further to the right is a cipher. This always hap-
pens when you divide a prime number larger than 5 by any other prime larger than 5. It can
happen in other cases, as well.
Endless repeating decimals
Your calculator can give you a glimpse of what an endless repeating decimal, also called a non-
terminating repeating decimal, looks like. The calculator program in a personal computer is
excellent for this purpose, because it displays a lot of digits.
Endless Decimals 101
