Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 year ago

# How do you convert from decimal form to fraction form?

I know the ones out of 100 but for example I got 4.5 for an answer but the answer key said 9/2 so I was wondering if there was a way to convert it to that.

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Here's a way that will work for any terminating decimal.

Write that as a number over 1.

4.5

----

1

Now you want to move the decimal point to the right one place, but you have to do that as well in the denominator.

45

---

10

Now you can reduce the fraction. Both the numerator and denominator have a common factor of 5, so divide both by 5.

9

--

2

You can't reduce any further, so that is the answer.

4.5 = 9/2

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• 4.5=450/100=45/10

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• The smallest decimal position is tenths (for the 5).

So we have 45 tenths.

45/10 . . . . . . . . cancel 5's

= 9/2

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• You can multiply ANY number by (1)

(10/10) = 1

4.5 (10/10) = 45/10

now reduce (remove factors of (1):

45/10 = (5/5) 9/2

so

9/2

====

OR another example, 0.005

0.005 (1000/1000) = 5/1000

This method works for any (nonrepeating) decimal.

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• Start with 4.5 over 100, and find the least common deniminator between the two numbers. it would be 9/200, not 9/2. To get the decimaal to a whole number, it must be multiplied by 2 (4.5x2=9). But then, the denominator must also be multiplied by 2 (100x 2 =200). 4.5/100 = 9/200.

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• 4.5

= 4 1/2

= 9/2

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• 4.5 = 45/10 = 9/2

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• 4.5 = x

10 * 4.5 = 10 * x

45 = 10x

45/10 = x

4.5 = x

45/10 = x

4.5 = 45/10

45/10 =>

(5 * 9) / (5 * 2) =>

9/2

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• Re-imagine your number as a fraction: 4.5/1

What would it take to make that a clean fraction? Aha! 4.5 is half of 9! To get there you'd double the numerator but you'll also have to double the denominator to match. So,

"Multiply by 1": 4.5 / 1 x 2 / 2 = 9 / 2

Okay, we got that out of the way. Now see if you can do the original problem without the calculator. :)

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• 4.5 with ".5" means it is some odd number of halves

4.5 = x/2

x = 2 * 4.5 = 9

4.5 = 9/2 as an improper fraction

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