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6th-8th Grade Math: Practice & Review55 chapters | 466 lessons

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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.

After watching this video lesson, you will be able to round larger numbers like a pro. Learn what the cutoff numbers are for rounding up and down to the nearest thousand, ten thousand and hundred thousand.

In math and when you go shopping, it is sometimes very useful to **round numbers**, to replace a number with a simpler number. For example, say you are shopping, and you are trying to figure out how much money you need. The items you currently have in your shopping cart cost $28.99 for shoes, $17.99 for a game, and $36.99 for a jacket. You might be able to easily add up 28.99 + 17.99 + 36.99, or you can round the numbers to the nearest tens and add 30 + 20 + 40. Which one can you do faster without writing it down and using just your head? For me, it is much easier to use the rounded numbers! In this video lesson, we will look at rounding to the nearest thousands, ten thousands and hundred thousands.

Let's begin with rounding to the nearest thousand. Remember the rules for rounding a decimal number that kept on going and going? You would pick a number to stop at, like perhaps two spaces after the decimal point. Then, you look at the digit directly to the right of the last digit you are going to write down. If this number is 5 or greater, then you round your last digit up. If it's less than 5, then you keep your digit the same. For example, to round the number 1.182945 to three decimal spaces, we want to stop at the 2. But should we write 2 or 3? We look at the digit directly to the right, the 9. Is this 5 or greater? Yes, so we round our 2 to a 3. Our rounded number is 1.183.

We can apply this same rule when we round larger numbers. When we round to the thousands then, we will round up if our number is 500 or greater, and we will round down if our number is less.

Remember, we are writing only numbers that are thousands. So, we have 0, 1,000, 2,000, 3,000 and so on. For example, if our number is 639, then we round up to 1,000, and if our number is 253, then we round down to 0. This is rounding to the nearest thousand. If we are higher than a thousand, we will round our thousand digit up if our last three digits are 500 or greater and keep our thousands digit if our last three digits are less than 500. For example, 1,865 rounds up to 2,000, and 3,145 rounds down to 3,000. If our number is 10,000 or larger, we keep our first digit and then round the thousand's digit based on our rule. So, 18,765 rounds up to 19,000, and 34,344 rounds down to 34,000.

We are essentially doing the same as we did before. We are looking at the digit directly to the right of the digit we want to round to. For the thousands, we look at the hundreds place. If this digit is 5 or greater, then we round up and if it is less than 5, then we keep our thousands digit the same. But since there may be numbers after the 5 that also affect our rounding, we use our rule instead of 500 or greater to round up and less than 500 to round down keeping the digit the same.

The rule for rounding to the nearest ten thousand is to look at the last four digits. If the last four digits are 5,000 or greater, then we round our ten thousands digit up, and if it is less than 5,000, then we keep our ten thousands digit the same. For example, 5,765 rounds up to 10,000. 43,567 rounds down to 40,000. 3,256 rounds down to 0, and 78,345 rounds up to 80,000. The numbers we would write here are 0, 10,000, 20,000, 30,000 and so on. If our number is a hundred thousand or higher, we keep all the higher digits and round our ten thousand's digit following our rules. So, 345,980 rounds up to 350,000, and 643,678 rounds down to 640,000.

For the nearest hundred thousand, we will look at the last 5 digits. If our last five digits are 50,000 or higher, then we round up, and if they are less than 50,000, then we round down and keep our hundred thousands digit the same. The numbers we write here are 0, 100,000, 200,000, 300,000 and so on. So, if our number is 78,323, then we round up to 100,000. If our number is 267,345, then we round up to 300,000. If our number is 743,325, then we round down to 700,000. For even larger numbers, we keep all of our larger digits and just focus on rounding the hundred thousand's digit following our rules. 3,567,080 rounds up to 3,600,000, and 5,620,134 rounds down to 5,600,000.

To review, to **round numbers** is to replace a number with a simpler number. To round to the nearest thousand, we look at the last three digits. If these digits are 500 or greater, then we round the thousands digit up, and if they are less than 500, then we round down, keeping the thousand's digit the same. To round to the nearest ten thousand, we look at the last four digits. If these digits are 5,000 or greater, then we round the ten thousands digit up, and round down if the digits are less than 5,000. To round to the nearest hundred thousands, we look at the last five digits. If the digits are 50,000 or greater, then we round the hundred thousands digit up, and round down if the digits are less than 50,000.

You should be able to round numbers to the nearest 1000, 10,000 and 100,000 after reviewing this video lesson.

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6th-8th Grade Math: Practice & Review55 chapters | 466 lessons

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