Convert 0.02¯¯¯¯¯
to a fraction.
Responses
2/99
2/101
1/5
1/50
The correct answer is 1/50.
wrong
Apologies for the mistake. The correct answer is 1/50. Would you like me to provide an explanation of how to convert 0.02¯¯¯¯¯ to a fraction?
wrong
I apologize for the confusion. Let's try again.
To convert 0.02¯¯¯¯¯ to a fraction, we can set it up as follows:
Let x = 0.02¯¯¯¯¯
Multiply both sides of the equation by 1000 to get rid of the repeating decimal:
1000x = 20.02¯¯¯¯¯
Now, we subtract the original equation from the multiplied equation:
1000x - x = 20.02¯¯¯¯¯ - 0.02¯¯¯¯¯
999x = 20
Finally, dividing both sides by 999 gives us the fraction:
x = 20/999.
Therefore, 0.02¯¯¯¯¯ is equal to 20/999.
To convert 0.02¯¯¯¯¯ to a fraction, we can set it up as an infinite repeating decimal. Let x = 0.02¯¯¯¯¯.
Step 1: Multiply both sides of the equation by 100 to eliminate the repeating decimal:
100x = 2.02¯¯¯¯¯
Step 2: Subtract the equation from step 1 from the original equation:
100x - x = 2.02¯¯¯¯¯ - 0.02¯¯¯¯¯
99x = 2
Step 3: Divide both sides of the equation by 99 to isolate x:
x = 2/99
Therefore, 0.02¯¯¯¯¯ is equal to 2/99.
To convert a recurring decimal like 0.02¯¯¯¯¯ to a fraction, we need to set up an equation based on the repeating pattern.
Let's call the decimal number x. We can express the repeating part as a fraction by subtracting x from a larger number that consists of the same repeating digit.
In this case, 0.02¯¯¯¯¯ can be represented as 0.02020202... because 02 repeats. So we have the equation:
x = 0.02020202...
Let's multiply both sides of the equation by 100 to shift the decimal point two places to the right:
100x = 2.02020202...
Now, we can subtract the original equation from this new equation to eliminate the repeating part:
100x - x = 2.02020202... - 0.02020202...
Simplifying the equation:
99x = 2
Divide both sides of the equation by 99 to solve for x:
x = 2/99
Therefore, the fraction representation of 0.02¯¯¯¯¯ is 2/99. Thus, the correct answer is 2/99.