The whole-number portion, 23, can be multiplied by 9,999, and the result put into the numerator of a
fraction. The denominator should then be 9,999, so we get
(23 × 9,999)/9,999= 229,977/9,999
That’s just the whole number 23 expanded into 9,999ths. Now we add the decimal part back in, so the
entire number becomes
229,977/9,999 + 8,604/9,999 = (229,977 + 8,604)/9,999
= 238,581/9,999
If you use a calculator that can display a lot of digits to divide out this fraction, you should get the original
expression: 23 followed by a decimal point, and then the sequence of digits 8, 6, 0, and 4 repeating.
Here’s a challenge!
There’s a less formal, but much quicker, way to do the decimal-to-ratio conversion described in the section
“Terminating decimal to ratio” earlier in this chapter. How does it work?
Solution
For reference, here is the original decimal expression again, with extra spaces on either side of the point
for easy reading:
3,588. 7601811
Move the point to the right until it’s at the end of the string of digits, leaving nothing beyond. Then delete
the point. You’ll get the whole number
35,887,601,811
Now make this the numerator of a fraction. Count the number of places you moved to the right to get
the point to the end of the string of digits. (In this case, it’s seven places.) Then in the denominator of the
fraction, write down a 1 followed by that number of ciphers. The result:
35,887,601,811/10,000,000
You can apply this method to any decimal expression you’ll ever see. The end result might not be in lowest
terms, but you can reduce it to lowest terms if you want.
Practice Exercises
This is an open-book quiz. You may (and should) refer to the text as you solve these problems.
Don’t hurry! You’ll find worked-out answers in App. A. The solutions in the appendix may not
represent the only way a problem can be figured out. If you think you can solve a particular
problem in a quicker or better way than you see there, by all means try it!
Practice Exercises 107
