# How to Estimate the Percent of a Number

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Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

Many of us deal with percentages on a daily basis, and we don't always have a calculator on hand to find them. In this lesson, we will look at how to estimate the percent of a number without the use of a calculator so we will be able to handle those instances more easily.

## Percent

When was the last time you went out to eat? Suppose you go out to eat with a friend and when the bill comes, it says it is \$51.64, but it also says that there is a 17% suggested gratuity. The gratuity is an example of a percent.

Percent means per hundred, and when we say that x is n percent of y, we mean that if we divide y into 100 equal parts, x takes up n of those parts. Alright, back to your dinner. You look at your friend, and he looks back at you. How much is 17% of \$51.64?

The good news is that you've got all the information you need to calculate the suggested gratuity.

In general, to find n percent of x, we follow these steps:

1. Divide n by 100.
2. Multiply the result by x.

Your friend breathes a sigh of relief when you pull a calculator out of your pocket. You want to calculate 17% of \$51.64, so we follow the steps. First, we divide 17 by 100.

Then we multiply the result by \$51.64

We see that the suggested gratuity is \$8.78.

## Estimating the Percent of a Number

We see that finding the percent of a number isn't too difficult. And although your cell phone (which you are never without, right?) does have a calculator, wouldn't you like to impress your friends by figuring out tips, sales prices, etc., without using a calculator?

Well, you're in luck! We can use a couple of tricks to estimate the percent of a number. Even though the estimate isn't exact, it can still give us a better picture of the situation.

If we are trying to find n percent of x, we can estimate this percent using the following steps:

1. Round both n and x up or down to numbers that are easy to work with.
2. Multiply the rounded numbers together.
3. Divide the result by 100.

This is actually perfect for when you are dining because you can round up or down based on the level of service you receive. Let's suppose that when you and your friend had dinner, you didn't have your calculator. You both decide the service was good, so when you round your 17%, you decide to round up to 20% since 20 is an easy number to work with. You also have to round your \$51.64. Since this is very close to \$50, and 50 is easy to work with, you round to \$50.

The next step is to multiply 20 by 50.

Lastly, we divide the result by 100.

We see that when we estimate 17% of \$51.64, we get \$10.00, which is pretty close to the exact answer of \$8.78. You leave a tip of \$10 and go about your evening with your friend.

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