# Rounding Numbers to the Nearest 1000, 10,000 & 100,000

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• 0:02 Rounding Numbers
• 0:56 To the Nearest 1,000
• 3:34 To the Nearest 10,000
• 4:49 To the Nearest 100,000
• 6:03 Lesson Summary
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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.

## Rounding Numbers

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.

## To the Nearest 1,000

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.

## To the Nearest 10,000

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.

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