Chapter 6: Decimals 79If you’re changing a fraction to a decimal and you find that you’ve gotten several digits in the
decimal form and you’re not getting a zero remainder, you’re not expected to keep dividing
forever. You might carry the division one place farther than you actually want and then round
your answer, understanding that this will give you an approximate, not exact, representation of
the fraction.
4
7 , for example, converts to 0.571428... and keeps going. You might round it to 0.571. On the other
hand, you might notice that as you divide, a pattern emerges.
7
9 converts to 0.77777... and keeps
repeating. To show that a pattern keeps repeating, you put a bar over the top, like this:
7
95 0.7.
To convert a decimal to a fraction, many times all you have to do is say the decimal’s name. The
decimal 0.37 is “37 hundredths,” so write it as
37
100. If possible, simplify the fraction. The decimal
0.8 is “eight tenths,” or
8
10. That simplifies to
4
5.Repeating decimals are a little trickier to convert to fractions. If you need to convert a repeating
decimal like 0.12121212... or 0.12 to a fraction, make the pattern (in this case, 12) your numerator,
and then count the number of digits in the pattern (in this case, 2 digits). Make your denominator
that many nines. 0.12 is equal to 12 over 2 nines or 0.12^12
99
5. Of course, simplify if you can.
- 12551299 334.
8 5.000
48
20
16
40
400.625CHECK POINT- Change to a decimal:
4
25 - Change to a decimal:
7
9 - Change to a fraction: 0.185
29. Change to a fraction: 0.123
30. Change to a decimal:
59
8