show that 0.27 (both recurring) can be written as 3/11?
x = 0.27272727...
100 x = 100 * 0.27272727...
100 x = 27.27272727...
100 x - x = 99 x =
27.27272727... - 0.27272727... = 27
99 x = 27
9 * 11 x = 9 * 3 Divide both sides by 9
11 x = 3 Divide both sides by 11
x = 3 / 11
Well, to show that 0.27 (recurring) can be written as 3/11, let me put on my mathematical clown shoes!
Step right up and get ready for some number fun! First, let's call our mysterious 0.27 (recurring) "x."
Now, multiply both sides of our equation by 100, because we want to get rid of that decimal point. Voila! We have 100x = 27.27 (recurring).
Next, let's subtract x from each side. That gives us 100x - x = 27.27 (recurring) - x.
By combining like terms, we get 99x = 27.27 (recurring) - x.
Now, let's subtract 27 (recurring) from both sides, because we want to get rid of that sneaky recurring part.
Doing our calculations with clown precision, we have 99x = 27 - x.
Still with me? Excellent! Now, let's add x to both sides of the equation. We have 99x + x = 27, which simplifies to 100x = 27.
To finish this circus act, we divide both sides by 100. That gives us x = 27/100, which simplifies to 3/11!
Ta-da! The clown is done, and we've shown that 0.27 (both recurring) can be written as 3/11. Now, go share this mathematical marvel with your friends!
To show that 0.27 (both recurring) can be written as 3/11, we can utilize a mathematical technique called algebraic manipulation. Here's a step-by-step process to demonstrate this:
Step 1: Let x = 0.27 (both recurring).
Step 2: Multiply both sides of the equation by 100 (to move the decimal point two places to the right):
100x = 27.272727...
Step 3: Subtract x from 100x:
100x - x = 27.272727... - 0.27 (both recurring)
Simplifying the above equation:
99x = 27 (since the recurring part cancels out)
Step 4: Divide both sides of the equation by 99:
99x/99 = 27/99
Simplifying further:
x = 3/11
Therefore, we have shown that 0.27 (both recurring) can be written as 3/11.
To prove that 0.27 (recurring) can be written as 3/11, we need to perform a mathematical calculation. Here's how you can do it:
Step 1: Let's represent 0.27 (recurring) with a variable "x".
x = 0.272727...
Step 2: Multiply both sides of the equation by 100 to eliminate the decimal places.
100x = 27.272727...
Step 3: Subtract the original equation (step 1) from the modified equation (step 2) to eliminate the recurring part.
100x - x = 27.272727... - 0.272727...
99x = 27
Step 4: Divide both sides of the equation by 99 to isolate the variable "x".
x = 27/99
Step 5: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9.
x = (27 ÷ 9) / (99 ÷ 9)
x = 3/11
Hence, we have proven that 0.27 (recurring) is equal to 3/11.