Convert 0.02¯¯¯¯¯
to a fraction. explain
To convert the repeating decimal 0.02¯¯¯¯¯ to a fraction, we can use the following steps:
Let x = 0.02¯¯¯¯¯
Multiply both sides of the equation by 100 (multiplying by 10^2 since there are two decimal places):
100x = 2.02¯¯¯¯¯
Subtract the original equation from the new equation to eliminate the repeating decimal:
100x - x = 2.02¯¯¯¯¯ - 0.02¯¯¯¯¯
99x = 2 (since the repeating decimals cancel out)
Divide both sides of the equation by 99 to solve for x:
x = 2/99
Therefore, 0.02¯¯¯¯¯ can be written as the fraction 2/99.
To convert a decimal number like 0.02¯¯¯¯¯ to a fraction, we can follow these steps:
Step 1: Write the decimal number as the numerator of the fraction.
In this case, the decimal number is 0.02¯¯¯¯¯, so the numerator of the fraction is 0.02¯¯¯¯¯.
Step 2: Determine the denominator of the fraction.
The denominator represents the place value of the last digit in the decimal. Since there is only one digit after the decimal point, the denominator will be 10 raised to the power of 1 (10^1), which is equal to 10.
Step 3: Simplify the fraction (if possible).
In this case, the fraction cannot be simplified any further.
Putting everything together, we can write 0.02¯¯¯¯¯ as the fraction 0.02¯¯¯¯¯/10.