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High School Algebra II: Homework Help Resource26 chapters | 281 lessons | 2 flashcard sets

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Learn how to use estimate values in this lesson. It can help you answer math problems that use more complicated numbers and even make it easier to split a check at the restaurant next time you are out with friends!

To **estimate** means to find something close to the correct answer. In other words, you are approximating. For example, the American statistic for the ideal number of children is 2.5. Now, obviously, nobody can have half a kid. We can estimate this exact statistic to either 2 or 3 children. We will discuss later under what situations you will estimate up or estimate down. To write estimate, we use the squiggly equal sign. Estimation can help you in various circumstances both in math and in real life.

When it comes to estimating in math, there is a general rule for you to follow. This **general rule** tells you to look at the digit to the right of the digit you want to estimate, and if it is less than 5 then you round down, and if it is greater than 5, you round up.

So, for example, if you wanted to round to the nearest whole number here, you would look at the digit right after the decimal since that is the digit to the right of the digit you want to round.

You can think to yourself, 'If I want to round to this place, what is the digit that is to the right of that?' For whole numbers, think what is the digit to the right of the whole number? It's the digit right after the decimal.

If we want to round these numbers to the nearest whole number, we'll need to look at the digit right after the decimal. Our general rule tells us that if our digit that is to the right of the digit we want to estimate is under 5, then we round down, and if it's greater, then we round up. Okay, that sounds easy enough.

Let's start rounding: 5.3 becomes 5; 3.7 becomes 4; 10.9 becomes 11. Oh wait. What about the 6.5? It's right in the middle. What do I do? For estimating purposes, **whenever you see a 5**, you will round up.

When you round down, you round down to your nearest number. When it came to rounding 5.3, I rounded it down to 5 because that was the closest one. I can draw it on the number line like this, and I can plainly see that 5 is the closest whole number to 5.3.

So rounding down doesn't mean going down one whole number, it just means going to the closest whole number which, when it comes to rounding down, means you keep the same whole number that you see. Rounding up means you go up to the next number. Like when I rounded 10.9 to 11. 11 is the closest whole number to 10.9. And, you can see it easily if you draw it out on a number line.

You can estimate to whatever place you want. Let's say you wanted to estimate to the nearest tens place. This means instead of estimating to the nearest whole number, you estimate to the digit that is in the tens place or the second one to the left of the decimal. To estimate this digit, you would look at the digit in the ones place because that is the digit to the right of the digit you want to estimate.

Estimating these numbers to the tens place, I would follow the same general rule as before, when we were rounding with decimals. Here, 456 becomes 460; 234 becomes 230; 789 becomes 790; 154 becomes 150; 845 becomes 850, and 565 becomes 560. Noticed how when I see a 5, I alternate rounding up and down? That is why 845 becomes 850, but 565 does not become 570. With all the others I followed the rule and did what I did when rounding to the nearest whole number.

What do you think we would do if we wanted to estimate to the hundreds place? Which digit would we look at?

Yes, we would look at the tens place to see if we need to round the hundreds place digit up or down. 160 estimates to 200 because the digit in the tens place is 6, which is greater than 5, and so we round up. 145 estimates to 100 because the digit in the tens place is a 4 which is less than 5 and so we round down. And if our number is 250, we can estimate to 300 since the number in the tens place is a 5, and it is the first 5 we have seen. If we need to estimate another number that also has a 5, we would want to round down the next time.

Estimates are helpful when you want to simplify math problems. Instead of solving 1.2 + 3.4, we can estimate to 1 + 3 and solve that instead. Isn't that much easier? In some problems, it tells you to estimate to a certain digit. It might tell you to round to the nearest whole number or the nearest hundred. Read your problem carefully to find out if you need to estimate.

Estimating is also useful in the real world. For example, when you are out with friends and need to figure out how to split a check so everyone pays a fair amount for all the food. When dealing with money though, it is best to always round up instead of following the general rule. You don't want to be short. Rounding down when it comes to money may mean you won't have enough. When dealing with money or anything else that you cannot have less of, always round up so you end up with more than less.

For example, say you went to the store with a five dollar bill. You grab a soda that costs $1.33 and a large bag of chips that costs $3.99, and before you get to the cash register, you want to make sure you have enough. If you followed the general rule for rounding to whole numbers, you would round $1.33 to $1 and $3.99 to $4. Since 1 + 4 = 5, you would think you would have enough, but you don't actually. By rounding $1.33 up to $2, you'll be able to see before you get to the cash register that you do not, in fact, have enough money, and that will save you some embarrassment.

The **general rule for estimating** is to look at the digit to the right of the digit you want to estimate. Estimating or rounding to the nearest whole number means looking at the digit to the right of the decimal. If you see a digit greater than 5, round up, and if it's less than 5, round down. When dealing with money though, rounding up will ensure that you will always have enough and not be short.

Step 1: Look at the digit to the **right** of the digit you want to estimate.

Step 2: **If** that number is **0-4**, then the digit you want to estimate **stays the same**. This is called rounding down. If not, move on to step 3.

Step 3: **If** that number is **5-9**, then the digit you want to estimate **increases by one**. This is called rounding up.

Done!

Check to be sure that you can accomplish the following goals at the end of this lesson:

- Describe the general rule for estimating
- Estimate a number involving a decimal point to the nearest whole number
- Estimate a three digit number to the nearest tens place and to the nearest hundreds place
- Identify real-life scenarios in which estimating may be useful

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High School Algebra II: Homework Help Resource26 chapters | 281 lessons | 2 flashcard sets

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