Convert Percentages and Decimals

Percent sign
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Converting percentages to decimals (and back) is a handy math skill, and it’s essential if you want to understand your finances. Whether you’re making quick estimates in your head, using a calculator, or modeling your car loan with a spreadsheet, you need to know how decimals and percentages are related.

Converting Percentages to Decimals

Most interest rates are quoted in terms of a percentage. But if you want to run calculations on that number, you’ll need to convert it to a decimal.

How do you make that happen?

Easiest – divide by 100: the simplest way to convert a percentage to a decimal is to divide the number (in percentage format) by 100.

Example: Convert 75% to decimal format. Divide 75 by 100 (this can also be written as 75/100 or 75 ÷ 100). The answer is 0.75, 75% = 0.75.

Search engines like Google and Bing make it easy to do quick calculations online, or you can also fire up your favorite calculator app if you prefer. To calculate with a search engine, simply “search” with the expression you’re trying to solve. For example, type in “75/100” or use this link.

Move the decimal: another way to convert a percentage to decimal format is to move the decimal 2 places to the left. Remember, if you don’t see a decimal, just imagine that it’s at the end – or far right – of the number (imagine that the decimal is followed by two zeroes if that helps).

Example: 75% is the same as 75.00%.

To convert it to decimal format, you’ll move the decimal 2 places to the left, so that it’s at the left of the 7. You’ll end up with .75 (or 0.75, if you prefer).

Once you do this enough, it will become natural and you’ll be able to do it instantly in your head.

What about more complex numbers? You’ll still just move the decimal over 2 places.

Let’s look at a few:

  • 100% becomes 1
  • 150% becomes 1.5
  • 75.435 becomes .75435
  • 0.5% becomes .005

Practical Example

Now, let’s put some of this knowledge to work.

Example: assume your bank pays 1.25% annual percentage yield (APY) on your savings account. How much will you earn over one year if you deposit $100? To find out, convert the interest rate to decimal format and multiply the result by the amount of your deposit (Hint: use an asterisk or “*” symbol to multiply when using a spreadsheet or search engine):

  1. 1.25% = 0.0125 (calculate with Google)
  2. 0.125 times $100 = $1.25 (calculate with Google)

You will earn $1.25 per year for every $100 that you deposit.

Example 2: you want to buy an item that normally costs $45. It is on sale at 30% off. How much would you save, and how much would it cost on sale? To find out, multiply the original price by 30%.

  1. 30% = 0.30
  2. 0.30 times $45 = $13.50 savings
  3. The sale price will be $45 minus $13.50, or $31.50

Alternatively, you could multiply the original price by 70% and get the same answer, because you'll only pay 70% of the original price.

The Big Picture

For better or worse, sometimes financial calculations like this only give you a rough idea of how much you’ll spend or earn (but it’s still useful for making quick, big-picture evaluations).

To be clear: converting a percentage to a decimal using the methods above is 100% accurate, but the question becomes what you do with that number after you’ve converted.

The next example shows how simply multiplying by a dollar amount can lead you astray.

Example: assume you’ll borrow $100,000 to purchase a home with a 30 year mortgage, and the interest rate is 6% per year. How much will you spend on interest each year? To get a rough idea (but not the true answer), convert the interest rate to decimal format, and multiply the result by the amount you borrow:

  1. 6% = 0.06
  2. 0.06 times $100,000 = $6,000

In fact, you won’t spend exactly $6,000 per year on interest unless you use an interest-only loan (the real answer is more like $5,966.59 for the first year). With most loans, you pay down the balance over time; with each monthly payment, a portion of the payment reduces your loan balance, and a portion covers your interest cost.

That process is called amortization, and you can read more about it starting with this page.

Ultimately, there will be a very brief period (just the first month) when you’ll owe the full $100,000 – after that you’ll owe less and less each month. Around year 15, you’ll only spend about $4,200 on interest.

All that said, $6,000 might be close enough for a quick estimate of how much you’ll spend on interest in the early years of your loan (so you can decide if it’s worth borrowing at 6%  – or borrowing on a credit card with a 20% interest rate, for that matter). But it’s certainly better to do exact calculations on your own so that you truly understand how your loan works. The idea is to get to a point where you can convert and multiply in your head (or on the back of a napkin) and quickly understand the big picture.

Convert Decimals to Percentages

What if you want to go the other way and convert a number from decimal to percentage format? As you might have guessed, just do the opposite of what you did above.

Multiply by 100: the easiest approach is to multiply a number in decimal format by 100.

Example: convert 0.75 to a percentage. Multiply 0.75 by 100 (this can be written as 0.75 x 100, or 0.75 * 100) to get 75, or 75%.

Move the decimal: to convert from decimal to percentage, move the decimal 2 places to the right.

Example: convert 0.75 to a percentage. 0.75 becomes 75, or 75%.