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
Circle P has a diameter of 20 feet. Circle Q has a diameter of 30 feet. What is the ratio of the circumference?
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?
A cylinder has a volume of 320 pi cu. in. and a height of 5". Find the radius of the cylinder.
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.