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Question 4256: Discuss how to convert a decimal into a fraction. Include in your discussion how you know at the start if the decimal can give you a fraction.
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Let me answer the second question first--it's easier than the first!!
First of all, any decimal must do one of three things. It must:
1. come out even (terminal decimals), like the decimals .23, .125, 7.2, etc.
2. repeat a pattern (repeating decimals), like the decimals .33333... , .252525...
or 3. never come out even and never repeat a pattern, like the values of pi, square root of 2, square root of 3, and many, many other such numbers.
The first two categories of numbers are called "rational numbers," and these numbers can be expressed in the form of a fraction. The third category of numbers are called "irrational numbers." These rational and irrational numbers together form the "real numbers," which comprise the numberline with which you are probably familiar if you have had any algebra classes at all.
1. To convert a terminating decimal to fraction, just realize what the decimals mean: .3 = 3/10,
.4 = 4/10 which reduces to 2/5
.49 = 49/100
.35 = 35/100, which reduces to 7/20
.025 = 25/1000, which reduces to 1/40
.002 = 2/1000, which reduces to 1/500
2. To convert a repeating decimal to a fraction, let x=the decimal, count the number of decimal places (digits) that repeat, and multiply both sides of this equation by 10, 100, or 1000 depending upon whether 1, 2, or 3 decimals repeat.
Example 1: x=.33333... (Notice only 1 digit repeats, so mult by 10)
10x=3.33333...
Subtract x=.33333... from each side:
10x = 3.33333...
- x -.33333...
9x = 3
Divide both sides by 9, and get x = 3/9, which reduces to 1/3, which everyone already knew!!
Example 2: x = .36363636...
Multiply both sides by 100, since two digits repeat the pattern.
100x = 36.363636...
- x - .363636...
99x = 36
Divide by 99, so x = 36/99, which reduces to 4/11.
Of course, the third category, that is irrational decimals, cannot be converted to fractions.
I strongly recommend that you buy a calculator for as low as $15 (a TI 30 or any graphing calculator) will do!! What I have explained here is a skill nearly lost to the calculator generation!!!
If you are still reading this LONG reply, have a very good day!!
R^2
Seminole Community College
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