00:00Please see the link in the description to download a worksheet for this video.
00:05If you've not already watched the video on the rounding rainbow,
00:08then we suggest that you watch that before viewing this video.
00:12When ranking something, we want everything to fit perfectly, so we measure distances
00:16very accurately. That applies to small wooden projects. And it applies to big projects,
00:22like planning where a new building will go. In both of these cases, we pay attention to
00:27each decimal in each place value. But there are other times when we don't need to know an exact
00:31number. We just want a rough idea of how big a number is. For example, the distance between New
00:36York and Los Angeles is 2,361 miles, but we often say it's about 2,000 miles. 2,000 miles is a much
00:45simpler number to say because many of the place values are zeros. When we simplify a number by
00:50turning some of its digits to zero, we call this rounding. We use rounding when we just want a
00:56rough idea of a number. For example, these signs show how many people live in three Minnesota towns.
01:03We can simplify these numbers by rounding them. We would say there are about 7,000 people who live
01:08in Belle Plaine, about 7,000 people who live in Jordan, and about 46,000 people who live in Shakopee.
01:16In this video, we'll learn how to round numbers that do not have a decimal point,
01:21what trailing zeros are, and how to round numbers that have a decimal point.
01:27We'll start by learning how to round numbers that do not have a decimal point.
01:31The water is deep in this area of the sea. The passengers ask the captain about how deep it is.
01:37Her depth finder tells her it's 698 feet deep in this area. That's too much detail for the passengers,
01:43so she wants to round it to the nearest hundreds place. What is 698 rounded to the nearest hundreds?
01:51For problems about place values, we recommend that you first draw the rounding rainbow.
01:58Let's start by writing the decimal point and drawing a dashed line. We'll write in the ones
02:02place above the dashed line. Then, we'll draw 5 dashed lines on the left, and 5 on the right.
02:09Each dashed line will be a place value. Then, we draw in the arches that connect the matching
02:14place values on each side. Now, we write the name of the place values for each arch. And finally,
02:20we write a reminder that those on the right side of the decimal have a suffix that says THS. We call
02:26this the rounding rainbow. Here's the original number we want to round. First, we circle the
02:32place value we want to round. In this case, we're going to round the hundreds place value. It's important
02:38to use a circle, as we'll explain shortly. One way to remember to use a circle is because a circle is
02:43round, and we're rounding a place's value. Then, we write the rhyme that tells us how to round. It says,
02:50look next door, if it's more than 4, then add one more. We'll draw a rectangle, which it is the shape
02:57of a door. This is next to the digit we want to round. In this case, the next door digit is a 9.
03:039 is greater than 4, so we'll add 1 to the digit we're rounding. That means the hundreds digit
03:09changes from a 6 to a 7. Here's what the rounded number looks like. Please note that all the digits
03:14to the right of the rounded digit become 0. So, the rounded number is 700 feet. When there are
03:21no digits to the right of the decimal point, we usually simplify the number further by writing it
03:26without a decimal point. The C is about 700 feet deep at this location. Next, we'll talk about
03:33what trailing zeros are. Here are two teddy bears. The price for the one on the right is $12.50.
03:41The one on the left has a price tag that says 12.00. What price is this?
03:46We do not say $12.00. Instead, we say $12.00. With a sensor zero, we only can say the amount.
03:58If we want, we can even leave off the decimal point and the zeros. That's because $12.00.
04:02$12.00 is equal to $12.00. We call these zeros trailing zeros. They're zeros that are on the far
04:11right side of the decimal point and with no other non-zero digits to the right. We can write these
04:17zeros if we want, but most of the time we choose not to write them or to say them. Next, we'll talk
04:22about how to round numbers that have a decimal point. This lady wants to know how far it is from
04:27the shore. Her husband just looked at his GPS and it says they are 4 and 8,375 10,000 miles from shore.
04:38That's too much detail for a casual conversation, so he wants to round it to the nearest tenth of a mile.
04:44What is this rounded to the nearest tenth of a mile?
04:50Here's the original number we want to round. First, we circle the place value we want to round.
04:56In this case, we're going to round the tenths place value. It's important to use a circle.
05:01Then, we write the round that tells us how to round. It says, look next door, if it's more than 4,
05:07then add one more. We'll draw a rectangle which is the shape of a door. This is next to the digit
05:13we want to round. In this case, the next door digit is a 3. 3 is less than 4, so we'll leave the 8 alone.
05:21That means the tenths digit stays as an 8. Here's what the rounded number looks like.
05:26Please note that all the digits to the right of the rounded digit become zero. These are trailing
05:31zeros. They're on the far right of the decimal point, and there are no non-zero digits to their
05:36right. We don't have to write trailing zeros, and it's simpler if we do not write them.
05:41Here's a simpler way to write the final answer. We pronounce this as 4 and 8 tenths. The boat is
05:48about 4 and 8 tenths of a mile from the shore. Thanks for your attention.
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