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Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

In this lesson, we'll discuss how to round decimals and use rounding decimals to estimate decimal products and quotients. We'll also look at some examples to help solidify our understanding of this process.

Decimals & Rounding

Do you ever notice that when you're giving someone the temperature, you always use a whole number? Even if your thermometer gave a reading of 74.7 degrees, you'd say, 'It's about 75 degrees outside.' Whether you realized it or not, you were rounding a decimal. Let's first talk about rounding decimals and then about estimating those products and quotients.

Returning to our example, when we said it was about 75 degrees outside, we used the whole number closest to 74.7. That is, we acknowledged that 75 is closer to 74.7 than it is to 74 degrees.

For instance, if it's 74.1 degrees outside, we'd most likely say it's around 74 degrees. This is exactly what's involved in rounding decimals. We simply round the decimal to the nearest whole number, or a number that does not include any fractions.

We can use the following rules to determine which whole number to use when rounding decimals:

When the decimal part of a number is lower than 0.5, round to the lower whole number.

When the decimal part of the number is 0.5 or higher, round to the higher whole number.

Pretty simple, huh? For instance, if we wanted to round the number 3.48, we would round to the number 3, because the decimal part, 0.48, is less than 0.5.

Decimal Products & Quotients

Now that we've discussed how to estimate decimals, it's time to see how to estimate decimal products and quotients. When estimating in both cases, we use the following steps:

Round the decimal numbers in the problem to whole numbers.

Perform the operation on the whole numbers found in step 1. This is the estimated, or approximate, answer.

Let's take a look at some examples to really solidify our understanding of this process.

Example #1

Let's say that you're at the grocery store and decide to pick up some chicken for dinner tonight. As chicken is on sale for $3.89 per pound, you decide to stock up and buy 5 pounds. When the sales associate weighs your chicken, it ends up being 5.12 pounds. You tell him 'close enough.'

So how much will those 5 pounds of chicken cost? The first step is to round the decimal numbers 3.89 and 5.12. We see that the decimal part of 3.89 is 0.89, which is greater than 0.5. This tells us that we need to round up to the nearest whole number, or 4.

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The decimal part of 5.12 is 0.12, which is less than 0.5. This tells us that we need to round 5.12 down to 5. We now have a simple multiplication problem:

4 x 5 = 20

So you're paying about $20 for 5 pounds of chicken. What a great deal!

Example #2

While you were shopping, you also bought 12.03 pounds of cat food for your fur baby at home. There was no price tag on the bin that you scooped the cat food out of, so you're not sure how much you paid per pound.

Your receipt says that the 12.03 pounds cost $24.34. We can estimate how much you spent per pound by estimating the decimal quotient 24.34 / 12.03.

First, we round the two decimal numbers. Here, 24.34 rounds down to 24, because 0.34 is less than 0.5. Similarly, 12.03 rounds down to 12, because 0.03 is less than 0.5. Now we divide 24 / 12 = 2.

You spent approximately $2 per pound on the cat food. Again, what a great deal!

Lesson Summary

Let's review. Most of the process of estimating decimal products and quotients involves rounding decimal numbers. To round decimal numbers, we use the following rules:

When the decimal part of a number is lower than 0.5, round to the lower whole number.

When the decimal part of the number is 0.5 or higher, round to the higher whole number.

To estimate decimal products and quotients, we follow these steps:

Round the decimal numbers in the problem to the nearest whole numbers.

Perform the operation on the whole numbers found in step 1, which is the estimated, or approximate, answer.

We encounter these types of problems quite a bit in our daily lives. That's why it's important to know how to estimate decimal products and quotients.

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