00:00This video is part of a Google Form quiz that teachers can assign to their students for
00:05homework. After the students submit their answers, then they can play a video like
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00:21please see the link in the description. This video is based on a question from an
00:26actual state exam. You may have one like this on your state exam. If you've not already watched the
00:31videos on the rounding rainbow and an introduction to rounding, then we suggest that you view those
00:37before watching this video. A student wants to round the number 54 and 6,758 ten-thousands.
00:45Which place value should the student round to so that the digit 6 appears two times?
00:51To answer this question, we'll look at each answer choice.
00:54Before we look at option A, let's make a rounding rainbow.
00:59Let's start by writing the decimal point and drawing a dashed line. We'll write in the ones
01:03place above the dashed line. Then, we'll draw five dashed lines on the left and five on the right.
01:10Each dashed line will be a place value. Then, we draw in the arches that connect the matching
01:15place values on each side. Now, we write the name of the place values for each arch. And finally,
01:21we write a reminder that those on the right side of the decimal have a suffix that says THS.
01:27We call this the rounding rainbow. Now, we're ready to look at option A.
01:33Let's round this original number to the hundredths place and see how many digits are six.
01:38Since we're going to round this number to the hundredths place,
01:40we first circle the hundredths place. That's the digit seven. Then, we write the rhyme that tells
01:46us how to round. It says, look next door, if it's more than four, then add one more.
01:52We'll draw a rectangle which is the shape of a door. This is next to the digit we want to round.
01:58In this case, the next door digit is five. Five is more than four. So, we will add one to seven,
02:04which totals eight. That means the hundredths digit changes from being seven to being eight.
02:10Here's what the rounded number looks like. Please note that all the digits to the right of the rounded
02:14digit become zero. When the digits that are farthest to the right of the decimal are zero,
02:20we call these trailing zeros. We can write these if we want, but it's more common to skip them.
02:26So, the simplified version of this rounded number looks like this. We pronounce this number as 54
02:31and 68 hundredths. Here's the rounded number next to option A. The directions tell us to find the
02:38answer option where the digit six appears two times. There is only one digit that's a six. So,
02:45this answer option is wrong. Now we're ready to look at option B. Let's round this original number to
02:52the tens place and see how many digits are six. Since we're going to round this number to the
02:56tens place, we first circle the tens place. That's the digit five. Then we write the round that tells us
03:03how to round. It says, look next door. If it's more than four, then add one more. We'll draw a rectangle,
03:10which is the shape of a door. This is next to the digit we want to round. In this case, the next door
03:16digit is four. Four is equal to four, so we will not add one to the digit that we're rounding. Instead,
03:23we'll leave it as it is. That means the tens digit stays as a five. Here's what the rounded number
03:28looks like. Please note that all the digits to the right of the rounded digit become zero. When the
03:34digits that are farthest to the right of the decimal are zero, we call these trailing zeros. We can write
03:40these if we want, but it's more common to skip them. So, the simplified version of this rounded number
03:45looks like this. We pronounce this number as 50. Here's the rounded number next to option B.
03:52The directions tell us to find the answer option where the digit six appears two times. There are
03:58no digits that are six. So, this answer option is wrong. Now we're ready to look at option C.
04:06Let's round this original number to the tens place and see how many digits are six. Since we're going to
04:12round this number to the tens place, we first circle the tens place. That's the digit six. Then,
04:18we write the rhyme that tells us how to round. It says, look next door, if it's more than four,
04:23then add one more. We'll draw a rectangle which is the shape of a door. This is next to the digit we want
04:30to round. In this case, the next door digit is seven. Seven is greater than four, so we'll add one to the
04:36digit we're rounding. That means the tens digit changes from a six to a seven. Here's what the
04:41rounded number looks like. Please note that all the digits to the right of the rounded digit become
04:46zero. When the digits that are farthest to the right of the decimal are zero, we call these trailing
04:52zeros. We can write these if we want, but it's more common to skip them. So, the simplified version of
04:58this rounded number looks like this. We pronounce this number as 54 and 7 tenths. Here's the rounded
05:06number next to option C. The directions tell us to find the answer option where the digit six
05:12appears two times. There are no digits that are a six. So, this answer option is wrong. Now we're
05:19ready to look at option D. Let's round this original number to the thousandths place and see how many digits
05:26are six. Since we're going to round this number to the thousandths place, we first circle the
05:31thousandths place. That's the digit five. Then, we write the rhyme that tells us how to round. It says,
05:38look next door, if it's more than four, then add one more. We'll draw a rectangle, which is the shape
05:44of a door. This is next to the digit we want to round. In this case, the next door digit is eight. Eight is
05:50greater than four. So, we'll add one to the digit we're rounding. That means the thousandths digit
05:56changes from a five to a six. Here's what the rounded number looks like. Please note that the
06:01digit to the right of the rounded digit becomes zero. When the digit farthest to the right of the decimal
06:06is zero, we call that a trailing zero. We can write it if we want, but it's more common to skip it.
06:12So, the simplified version of this rounded number looks like this.
06:16We pronounce this number as fifty-four and six hundred seventy-six thousandths.
06:21Here's the rounded number next to option D. The directions tell us to find the answer option
06:26where the digit six appears two times. There are two digits that are six. So, this answer option
06:33is correct. Choice D is correct. Thanks for your attention.
