Question

write the following decimals as fraction in ther lowest term 2.8

Answer 1

2.8=28/10=14/5
is the right answer

Answer 2

How do you express a decimal as a fraction in the lowest terms, for example, 0.237, repeating?

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7 ANSWERS



Steven Smith, Earned 98% or higher in all my math classes at UCMO.

Updated Oct 27, 2017 · Author has 2.4k answers and 1.1m answer views

Here is a technique that will allow you to convert any number that eventually becomes a repeating decimal into an improper fraction.

You define the number you are looking at as a variable, let’s say xx.

x=0.237237237…x=0.237237237…

You look at the period of the repeating digits. For example 0.237237237237… would be a period of 3.


0.237237237….repeating = 1x

multiplying x by 1000 moves the decimal point three places to the right.

237.237237….repeating = 1000x

now take 1000x and subtract 1x

(237.237237237… - 0.237237237….) = (1000x - 1x)

The entire string of digits after the decimal point is the same for each, and subtracting gives all 0’s after.

Subtract.

237 = 999x

Divide both sides by 999 to solve for x.

237999=999x999=1x=0237999=999x999=1x=0.237237....237237... repeating

0.237237...0.237237... (repeating) = 237999237999

but this is not in lowest terms if 237 and 999 have any common factors. I can see that they each divide evenly by three since the sums of their digits each divide by three.

so…

0.237237...0.237237... (repeating) = 237999=3⋅793⋅333=79333237999=3⋅793⋅333=79333