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## Numbers & Operations - The Real & Complex Number Systems 211-217

### Course: Numbers & Operations - The Real & Complex Number Systems 211-217 > Unit 1

Lesson 7: Rounding decimals# Rounding decimals on the number line

Learn how to round decimals using a number line, visually showing which whole number, tenth, hundredth, or thousandth is closest. Building off intuition of rounding rules and connect rounding to the nearest place value on the number line.

## Want to join the conversation?

- how can we round a decimal to one and nearest hundredth.(33 votes)
- it's impossible without point A(3 votes)

- how do we round to the ten thousand place(8 votes)
- Hi!

This is how it would work

To round numbers to the nearest ten thousand, make the numbers whose last four digits are 0001 through 4999 into the next lower number that ends in 0000. For example 54,424 rounded to the nearest ten thousand would be 50,000.

Hope This Helps!(41 votes)

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- how do we round decimals to nearest tenth(2 votes)
- So say you had 359, we no that the 5 is the tens place so we look one way to the right and that is 9,(because 9 is 5 or larger we will round up to then nearest ten) = 360.

However if the number was 344 we would round down to the nearest ten (Because 4 is 5 or bellow) = 340

Let's do another one that is a bit different,

236.986 round to the nearest ten(It is important to remember that tens is before the decimal point and tenths is after the decimal point)

= 240, why? because we had the number 236 and 6 is larger than 5 so we round up, why did we get rid of the decimal points? Well this applies in all cases if you were to round 26,345 to the nearest thousand it would be 27,000, because you only focusing on the thousands but nothing else.

(If you still don't understand watch this video:

Worked example: rounding decimal to the nearest tenth.

(If you have any more questions do ask)

Hope this answers your question.(20 votes)

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- My promblem didn't have the blue lines for the tenths, so i was a little confused. But your video helped a lot and i love Khan Academy soooooooooooooooooooo much!!💙🙂(10 votes)
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## Video transcript

- [Instructor] So we are
asked to drag the point to 12.5 on the number line, so let's see. Let's see, this is 12, and 12.5
is halfway between 12 and 13 then say say what is 12.5
rounded to the nearest 10? Well, what's cool about
this is you can see on the number line that our
tens are in this blue hash. So we have 10 and then 20
and we're between 10 and 20 and which one are we closest to? Which is literally the nearest 10? Well, you can see we are
closer to 10 than we are to 20 so you would say 10, and this
helps us build an intuition for what rounding to the
nearest 10 even means because you might know a rule like, hey look, you go one place
less than the tens place, which would be the one's place and if it's less than five
there you round down to 10. If it's five or greater
you round up to 20. But you see why over here,
we are just closer to 10. Let's do another example here. So here it says drag the point to 0.136. So this is 0.13, this is
0.14, so this is 13 hundredths and this is 14 hundredths, now let's see. There's one, two, there, four, five, six, six, seven, eight, nine, ten. So these are, you could think
of it as the ten thousandths between these two hundredths. So we want to go 13 hundredths and then another six thousandths. So let's see, we go one,
two, three, four, five, six. Just like that, and then
they say what is this number? 136 thousandths or 0.136 rounded
to the nearest hundredth. Well, we have our hundredths in blue here, and which one are we closer to? Well, we're closer to 14 hundredths, 0.14. And that's consistent with
what we've seen in other cases where you look at the thousandths place and if it's five or greater you round up. In this case, you would
round up to 14 hundredths. Let's do a few more examples here. So let's say that, so they're asking us which point is at 44.197
on the number line? So let's see, that's going
to be between 44 and 45, so it's right over here, 44.197,
so that would be point C. And then they say, what is 44.197 rounded to the nearest whole number? Well, there's a couple of
ways to think about it. You could just look at the tenths place and say look, that's less than
five so we round down to 44 or a more intuitive way
of thinking about it is like look, point C is
the number we care about. That is 44.197. What's the closest whole number to it? Is it closer to 44 or is it closer to 45? Well, it's clearly closer to 44, so that's another reason
why 44 makes a lot of sense. Let's do another example. Let's say that we want to, so they say, what is A rounded to
the nearest thousandth? What is A rounded to
the nearest hundredth? So A is right over here,
let's get our bearings. So 0.7, that's seven hundredths. This is eight hundredths right over here. And then between them, let's see, this looks like it's
zero, so you can view this as 70 thousandths, 71
thousandths, 72 thousandths, 73 thousandths, 74 thousandths, and so on. So this is between 78
thousands and 79 thousandths. So if we round to the nearest thousandth it looks closer, in fact,
it's definitely closer to 78 thousandths than
it is to 79 thousandths. So I would say this is
0.078, or 78 thousandths. That's closer, that's
the nearest thousandth. What is A rounded to
the nearest hundredth? Well, what are the hundredths
that it's in-between? It's in-between seven
hundredths and eight hundredths. And which one is it closer to? Well, it's closer to
eight hundredths, 0.08. So once again, the whole
point of this video is to appreciate when people say round to the nearest whole
number, to the nearest 10, to the nearest thousandth,
to the nearest hundredth, you can think of it on a
number line and just say, well, what is the closest hundredth to it? Or what hundredth is it closest to? Which thousandth is it
closest to on the number line?