# 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.
1. Write the percent without the percent symbol.
2. 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 = 102, 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.