# Percent to decimal

Converting a percent to a decimal involves simply shifting the decimal place by dividing the percent by 100. The term "percentage" is derived from the Latin "per centum" which means "by a hundred," or, per hundred. Thus it makes sense that converting a percent to a decimal involves dividing by 100.

### Methods for converting a percent to a decimal

- Long division - while this method can be used, and is also relatively simple to do, it is not efficient.
- Shifting the decimal place two places to the left - this method requires some base understanding of the decimal numeration system, but is much more efficient than performing long division.
- Write the percent without the percent symbol.
- Shift the decimal point two place values to the left. This is the percent in decimal form.

In the decimal numeration system, each decimal place represents a power of 10. As we move left of the decimal point, the place value increases by a factor of 10. Conversely, as we move right, the place value decreases by a factor of 10. 100 = 10^{2}, so dividing by 100 (which makes our number smaller) means that we move the decimal point two place values to the left, so that we are decreasing the number by a factor of 100:

Example

Say we want to convert 8.25% to a decimal. We need to shift the decimal place two spaces to the left:

So, 8.25% in decimal form is 0.0825.

Conversely, to convert a decimal to a percent, we simply shift the decimal point two place values to the right, and add a % symbol.