# Convert Percentages and Decimals

Knowing how to convert percentages to decimals and back again comes in handy as a valuable math skill, and it’s certainly helpful for understanding your finances. Whether you’re making quick estimates in your head, using a calculator, or modeling your car loan in a spreadsheet, you need to know how decimals and percentages are related.

Examples follow below, and you can also do quick conversions using one of many free online calculators.

### Converting Percentages to Decimals

Most interest rates are quoted and advertised in terms of a percentage. But if you want to run calculations using those numbers, you’ll need to convert to decimal format.

There are several ways to 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 percent to decimal format.

- Divide 75 by 100 (this can also be written as 75 / 100 or 75 ÷ 100)
- The result is 0.75, meaning that 75 percent is the same as 0.75

Search engines like Google and Bing also 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, “search” with the expression you’re trying to solve. For example, type in “75/100” or use this link to solve the example above.

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

*Example:* Convert 75 percent to decimal format.

- 75 percent is the same as 75.00 percent
- To convert to decimal format, move the decimal two places to the left so that it’s on the left of the 7
- The result is .75 (or 0.75, if you prefer)

After you do this several times, 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 two places. A few more examples:

- 100 percent becomes 1 (or 1.00)
- 150 percent becomes 1.5
- 75.435 becomes .75435
- 0.5 percent becomes .005

### Practical Example

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

*Example:* Assume your bank pays 1.25 percent 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 numbers when using a spreadsheet or search engine):

- 1.25 percent = 0.0125 (calculate with Google)
- 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 percent off. How much would you save, and how much would it cost on sale?

To find out, multiply the original price by 30 percent.

- 30 percent = 0.30
- 0.30 times $45 = $13.50 savings (0.30 * $45 = $13.50)
- The sale price will be $45 minus $13.50, or $31.50

Alternatively, you could multiply the original price by 70 percent and get the same answer, because you'll only pay 70 percent of the original price. To arrive at 70 percent, you’d subtract the 30 percent savings from one. This works because one is the same as 100 percent or the full, original pre-sale 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, although that estimate is still useful for making quick, big-picture evaluations.

Converting a percentage to a decimal using the methods above is 100 percent accurate, but the question becomes what you do with that number *after* you’ve converted. The next example shows how simple calculations with dollar amounts 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 percent per year. How much will you spend on interest each year?

To get a rough idea (but not the exact answer), convert the interest rate to decimal format, and multiply the result by the amount you borrow:

- 6 percent = 0.06
- 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 for most fixed-rate home loans is more like $5,966.59 for the first year.

With standard home and auto loans, you pay down the debt over time using level monthly payments. With each payment, a portion of the payment reduces your loan balance, and the remaining portion covers your interest cost. That process is called *amortization*, and you can read more about how it works and how to build an amortization table.

Since you’re paying down the loan balance, there will only be a brief period (just the first month) when you owe the full $100,000. After that, you’ll owe less and less each month, and your interest costs will decrease accordingly. For example, around year 15, you’ll only spend about $4,200 on interest.

All that said, $6,000 might be close enough. You’ll get a quick, informal estimate of how much you’ll spend on interest in the early years of your loan, and you can decide if it’s worth borrowing at 6 percent — or borrowing on a credit card with a 20 percent 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 goal 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 as well as the finer details.

### 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)
- The result is 75, or 75 percent

See that done with the Google calculator.

**Move the decimal: **Another way to convert from decimal to percentage format is to move the decimal two places to the right.

*Example:* Convert 0.75 to a percentage.

- 0.75 becomes 75 (which can also be 75.00 or 75 percent)