How can I convert a percentage into a decimal without moving the point the wrong way?
Quick answer
A percent means “per 100,” so convert a percentage to a decimal by dividing its number by 100. For a shortcut, move the decimal point two places left and remove the percent sign. For example, 6.4% becomes 0.064. Check the size: a percentage below 100% should become a decimal below 1; if your answer is larger, recheck the direction. [S1]
The question, the details, the next step.
I keep second-guessing whether to move the decimal left or right. What is the rule for turning a percentage into a decimal?
Divide the percentage number by 100. The word “percent” means “per 100,” so 7% is 7/100, which is 0.07. [S1]
The shortcut is to move the decimal point two places to the left, then drop the percent sign. Moving it left makes the number smaller, which fits dividing by 100. For instance, write 7 as 7.0, then move the point two places left: 0.07.
Think of the decimal point as shifting, rather than the digits travelling anywhere: 7.0 → 0.70 → 0.07. If there aren’t two digits to the right of the point, add zeroes as needed.
Could you show that with a percentage that already has a decimal point? I’m worried I’ll shift it too far.
Try 6.4%. The starting number is 6.4; shift its decimal point two places left, adding a leading zero where needed:
6.4 → 0.64 → 0.064
So 6.4% = 0.064. Another way to check the calculation is to divide: 6.4 ÷ 100 = 0.064. These are two ways to do the same conversion, not two extra steps to apply one after the other. In particular, don’t first divide by 100 and then shift the point again.
How can I tell if I moved the point the wrong way or placed it one spot off?
Use a size check. Percentages below 100% convert to decimals below 1; percentages above 100% convert to decimals above 1; 100% converts to 1. This follows from writing the percentage number over 100. [S1]
For example, if you convert 6.4% to 0.64, notice that 0.64 is below 1 but much larger than 0.064. The division check resolves the place-value question: 6.4 ÷ 100 = 0.064, so 0.64 is ten times too large. If you got 640, you moved in the wrong direction: dividing by 100 should make a positive number smaller, not larger.
Can I use a repeatable method when I’m doing several conversions?
Yes. Keep the rule and the check separate: first convert, then test whether the result has the right size. Here’s a copyable example:
18% = 18 ÷ 100 = 0.18
The answer is below 1, as expected for a percentage below 100%. For 125%, the same rule gives 125 ÷ 100 = 1.25, which is above 1, as expected. Writing the division alongside the decimal shift makes it easier to spot whether you shifted twice or went the wrong way. These examples show the conversion rule; they don’t establish how a percentage should be interpreted in a particular real-world situation.
A practical checklist
Write the percentage number as a value to divide by 100.
Move the decimal point two places left, adding zeroes if needed.
Check that the result matches division by 100.
Check the size: below 100% gives less than 1; above 100% gives more than 1. [S1]
If the result seems off, redo the division and check the decimal-place shift.
A few more useful answers
What if the percentage is a whole number, like 5%?
Treat 5 as 5.0, then move the point two places left: 5% = 0.05. You can check by dividing 5 by 100. [S1]
Does a percentage greater than 100% become a decimal less than 1?
No. For example, 125% ÷ 100 = 1.25, which is greater than 1. The size check helps catch an answer with the point shifted too far left. [S1]
Should I keep the percent sign after converting?
No. The converted value is written as a decimal without the percent sign: 18% becomes 0.18.
Sources
References used for this guide.
- [S1] 6.1 Understand Percent — Prealgebra 2e openstax.org · Checked