Mathematics, 15.07.2019 09:40 brittneyhiebert2543

Write the number 0.21212121.. as a fraction let x=

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We know that numbers with periodic decimals (there are decimals that repeat infinitely) can be written as a fraction of two integer numbers.

Here we have the number:

0.212121...

Where the decimals "21" are repeating decimals, and we want to write this as a fraction.

And we will find that the fraction form of this number is: 21/99

To find it, first let's define:

x = 0.212121...

Now we need to multiply this by 10^n, where n is the number of repeating decimals, here we have two (2 and 1) then n = 2.

Now we need to multiply:

x×10^2 = x×100 = (0.2121...)×100 = 21.212121...

Now we can subtract the original number so we get:

x×100 - x = x×99 = 21.212121... - 0.212121... = 21

Then we just found that:

x×99 = 21

Solving for x, we get:

x = 21/99 = 0.212121...

Then the fraction that we want to find is 21/99

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Answer from: audreymvarney

There are 2 repeating decimals, so you will need a 1 followed by 2 zeros which is 100. You'll use 100 soon to multiply an equation.

Let's call the decimal number x.

Write

        x =     0.212121...

Then multiply the equation above by 100, and write it above that equation.
You end up with

    100x = 21.212121...
          x =   0.212121...

Now set it up as a subtraction, and subtract the second equation from the first equation:

    100x = 21.212121...
          x =   0.212121...
-
      99x = 21

Now solve for x. Divide both sides by 3:

33x = 7

Divide both sides by 33:

x = 7/33

Since x = 0.212121..., an d x = 7/33, that means 0.212121... must equal 7/33.

the fraction is 7/33

Answer from: Quest

need more information

step-by-step explanation:

Answer from: Quest

so, converting firstly the mixed fractions to improper fractions and then "adding".

$\bf \stackrel{mixed}{2\frac{9}{10}}\implies \cfrac{2\cdot 10+9}{10}\implies \stackrel{improper}{\cfrac{29}{10}}~\hfill \stackrel{mixed}{5\frac{4}{15}}\implies \cfrac{5\cdot 15+4}{15}\implies \stackrel{improper}{\cfrac{79}{15}} [-0.35em] ~\dotfill$

$\bf -\cfrac{29}{10}+\left( -\cfrac{79}{15} \right)\implies -\cfrac{29}{10}-\cfrac{79}{15}\implies \stackrel{\textit{using the lcd of 30}}{\cfrac{-(3)29-(2)79}{30}}\implies \cfrac{-87-158}{30} \cfrac{-245}{30}\implies -\cfrac{49}{6}\implies -8\frac{1}{6}$

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