What is 0.22 as a fraction? | Thinkster Math (2024)

Step 1:

The first step to converting 0.22 to a fraction is to re-write 0.22 in the form p/q where p and q both are positive integers. To start with, 0.22 can be written as simply 0.22/1 to technically be written as a fraction.

Next, we will count the number of fractional digits after the decimal point in 0.22, which in this case is 2. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 0.22/1 each by 10 to the power of that many digits. For instance, for 0.45, there are 2 fractional digits so we would multiply by 100; or for 0.324, since there are 3 fractional digits, we would multiply by 1000. So, in this case, we will multiply the numerator and denominator of 0.22/1 each by 100:

In the given number 0.22... there is one repeating digit which is 2. So, by using the repeating decimal to fraction trick, we know that 0.22... can be written as 2/9.

To change a decimal to a percent, we multiply by 100. This is the same as moving the decimal point two places to the right. To change the decimal 0.22 to a percent, we move the decimal point two places to the right and get 22%.

0.2222… X 10 = 2.2222… Then subtract 0.222… from 2.222… and you get 2! The repeating numbers are gone! You also have to subtract the 10 multiplier (remember we multiplied 0.222… by 10?) from the 1 multiplier (because we made no change to the 0.222… same as multiplying by one) to get 9; so the answer is 2/9.

Percent means “per 100,” or “divide by one hundred.” So 22% is equal to 22/100. Notice how 22 and 100 are both even numbers, which mean they are divisible by two. That means you can simplify the fraction to 11/50.

Here, 0.23 consists of 2 digits after the decimal point and the last digit is non-zero so this result is valid. Now, we will multiply the numerator and denominator of the number 0.23 by ${10^n} = {10^2} = 100$. Therefore, $\dfrac{{23}}{{100}}$ is the required expression of 0.23 in terms of vulgar fraction.

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