# Estimating Decimal Products and Quotients

Instructor: Laura Pennington

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

In this lesson, we will see how to round decimals, and we will use rounding decimals to estimate decimal products and quotients. We will look at examples to help solidify our understanding of this process.

## Decimals and Rounding

I don't know what the temperature is in your neck of the woods, but with it being summer where I am, it is extremely hot! Do you ever notice that when you are telling someone the temperature outside, you always give them a whole number? Even if you looked at your thermometer and it said that it was 74.7 degrees, if you were to report the temperature to someone you would say it's about 75 degrees outside. This is actually a process of rounding decimals.

Ultimately, in this lesson, we want to see how to estimate decimal products and quotients, but we will soon see that rounding decimals is a big part of doing this. Therefore, let's first talk a bit about rounding decimals, and then we will explain estimating those products and quotients.

Okay, back to our temperature example. When we said that we would say it is about 75 degrees outside if it is actually 74.7 degrees, notice that we went to the whole number closest to 74.7. That is, we know that 75 is closer to 74.7 than 74 is. For instance, if it was 74.1 degrees out, we would most likely say it's around 74 degrees. This is exactly what is involved in rounding decimals. We simply round our decimal to the nearest whole number. Technically, we use the following rules to determine which whole number to round to.

We see that when the decimal part of a number is lower than 0.5, we round to the lower whole number, and when the decimal part of the number is 0.5 or higher, we 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.

## Estimating Decimal Products and Quotients

Alright! We've seen how to round decimals, so now comes the exciting part! We get to see how to estimate decimal products and quotients. The good news is that we are now comfortable with rounding decimals, because really, this is the main part of estimating decimal products and quotients.

In both the case of decimal products and quotients, when we are estimating, we use the following steps:

1. Round the decimal numbers in the problem to whole numbers.
2. Perform the operation on the whole numbers you found in step 1. This is your estimated, or approximate, answer.

See? Told you that rounding was the main part of this process! Let's take a look at some examples to really solidify our understanding of this process.

## Examples

Let's say that you just finished reading this lesson, and head to the grocery store to pick up a few things. One of the things you are buying is some chicken for dinner tonight. You head over to the meat department and see that chicken is on sale for \$3.89 per pound. You decide to stock up and buy 5 pounds, intending to freeze it for later use. When the worker measures out your chicken, it ends up being 5.12 pounds, so you tell him 'close enough'. You then go about the rest of your grocery shopping. While doing so, you are trying to figure out the approximate amount that you will be spending on the chicken. In other words, you are trying to estimate the decimal product 3.89 * 5.12.

You thank your lucky stars that you just read this lesson before leaving the house and get to work estimating this product. 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, so we know that we need to round up to the nearest whole number, so we round 3.89 to 4. The decimal part of 5.12 is 0.12, which is less than 0.5, so we round 5.12 down to 5. We now have the simple multiplication problem of 4*5, which we know is 20.

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