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

Answers

Answer 1
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.

Answer: the fraction is 7/33
Answer 2

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

If you want to learn more you can read:

https://brainly.com/question/11155736


Related Questions

Circle P has a diameter of 20 feet. Circle Q has a diameter of 30 feet. What is the ratio of the circumference?

Answers

Perimeter of circle = 2πr
2:3.



Answer:

The ratio of the circumferences of Circle P to Circle Q is [tex]\( \frac{2}{3} \).[/tex]

Explanation:

The circumference of a circle is given by the formula \(C = \pi \times d\), where [tex]\(d\)[/tex] is the diameter.

For Circle P with a diameter of 20 feet, the circumference is:

[tex]\[ C_P = \pi \times 20 \][/tex]

For Circle Q with a diameter of 30 feet, the circumference is:

[tex]\[ C_Q = \pi \times 30 \][/tex]

To find the ratio of the circumferences of Circle P to Circle Q, we divide the circumference of Circle P by the circumference of Circle Q:

[tex]\[ \text{Ratio} = \frac{C_P}{C_Q} = \frac{\pi \times 20}{\pi \times 30} \][/tex]

[tex]\[ \text{Ratio} = \frac{20}{30} = \frac{2}{3} \][/tex]

So, the ratio of the circumferences of Circle P to Circle Q is [tex]\( \frac{2}{3} \).[/tex]

A water tank holds 18,000 gallons. How long will it take for the water level to reach 6000 gallons if the water is used at an average rate of 450 gallons per day?

Answers

2.18,000-6,000=12,000. and then you divide 12,000 by 450 and you get 26 2/3 days.
If the original 18,000 gal of water is draining at a rate of 450 gal/day, we begin by calculating how many gal it needs to drain:
18,000-6,000 = 12,000 gal
Now setup 12,000 gal/1 × 1 day/450 gal, in order to cancel out gallons and have our result in days.
So 12,000/450 = 240/9 = 26.66 days, or a full 27 days rounding to the day

A cylinder has a volume of 320 pi cu. in. and a height of 5". Find the radius of the cylinder.

Answers

Answer:

The radius of cylinder is 8 inches.

Step-by-step explanation:

We have given,

Volume of cylinder = 320π   cubic inches

Height of cylinder = 5 inches

We know, Formula for volume of cylinder as : V =πr²h

where r is radius of cylinder and h is the height of cylinder.

So, We can plug values for V and h to get radius of cylinder.

i.e  V = πr²h

320π = πr²* 5

Solving for r.

We get,

320 = r² * 5

320/5 = r²

64 = r²

or r = ±8 , Since radius of cylinder can not a negative number so we neglect -8.

Hence the radius of cylinder is 8 inches.


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