# If you divide 100 by 3, you get 33.3333333…, but if you miltiply 33.3333333 it equals 99.9? how makes sense?

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How does this make mathematical sense?

• Technically, it equals 99.999999999999999999999…. on into infinity, which for all intents and purposes is the same as 100. Your calculator is just limited by a finite memory and so it cannot show you that.

• Division is all about equal parts. Divide 100 in 3 equal parts. You have 100 dollars and you want to divide them among your 3 friends in equal parts. Unfortunately there’s no way to do that. So the REAL LIFE division will be 33.3 + 33.3 + 33.4 = 100 . Mathematically, you get 33.3333333, which is an approximation .. and you get 33.33333 so that way.. when multiplied by 3… You’re gonna get the closest number to 100 which is 99.99999999 . And 99.9999999 is approximately 100. So that.

• It makes sense. Understand that 3 is no closer to infinity then 9. It all comes down the the infinite number of 3’s you multiply by. The more you get or closer to infinite number of 3’s you use, the closer it gets to = 100. This is called an asymptotic line.

• 100 / 3 gives you a periodical decimal number, whose period is infinite.

The more decimals you work out, the more accurate the answer will be, but you will never get back to 100

The best way to show this number on a problem is keep the fraction form so that you do not add errors to your answer by dividing this number too early. Maybe you can simplify it further on in the work

Source(s): maths teacher
• ah! you guys are all using decimal answers to prove the reverse… hmmm

since the fraction 100/3 can be reduced to 33 1/3 as a mixed fraction, it is then easy to see that if you multiply this same mixed fraction by 3, then your answer in return is 100 !

fractions are not always absolute numbers!!!!!!!

they are just a way to represent a particular number or idea!

same as PI! pi=3.14…….

AAAND! FOR ALL INTENSIVE PURPOSES, 99.999999999999999999… IS NOT 100!

not at all! not even close! not in this example!

stick to FRACTIONS when you think of these things and try not to convert a fraction into a decimal and then back into a fraction!!!

• 3 * 33.33333… = 99.9999999…..

100 ÷ 3 = 33 1/3 = 33.333333….

You changed a repeating, never ending decimal(33.3333….) to a terminating decimal(33.3333333). That’s why it doesn’t seem to make sense.

• Actually it equals 99.999999999, which for all practical purposes is the same as 100

• 99.999999999999999999……………………… is 100. It isn’t “basically” 100 or “the limit” to 100 or “for all intents and purposes” can be considered as 100. It is 100.

Proof:

99.99999……. = x

999.999999…….. = 10x

999.999999…… – 99.9999999……… = 10x – x

900 = 9x

100 = x

99.9999….. = x

100 = x

99.9999…… = 100

• in the limit, 99.9999999999999999999999999999999999999999 is 100

• That’s because is it 33.333 continuous. You will never be able to multiple those numbers back together because you will never be able to get enough 3’s. 33.333 continuous x 33.333 continuous = 99.99 continuous.

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