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

Lesson 5: Decimals in different forms# Visual understanding of regrouping decimals

Explore the concept of place value in decimals, focusing on how to regroup value from one place to another. Understand the relationship between ones, tenths, and hundredths in decimal numbers.

## Want to join the conversation?

- How do you change a decimal by its value?(33 votes)
- you look to the left of the decimal and if it is 5 or more 4 or less let it rest(39 votes)

- can we have decimals like this 3.0485684948593850 yes or no(25 votes)
- Yes, decimals can have any number of digits after the decimal point. They can even have infinitely many digits after the decimal point.

Have a blessed, wonderful day!(25 votes)

- I got the correct answer and it says it is wrong(15 votes)
- try refreshing the site or as a adult or report a problem when your doing a exercise(10 votes)

- 3.47 = 3 ones and 4 tenths and 7 hundredths

If you regroup those to 3 ones and 14 tenths and 7 hundredths. What would it looked like on decimal?

3.147 ? 🤔😕(14 votes)- You went from having 4 tenths, to having 14 tenths. If you wanted to do that, you would have to say 2 ones, 14 tenths, and 7 hundredths, because you borrowed 10 tenths (1 whole) from the 3 ones.(8 votes)

- thanks! i learned alot(7 votes)
- reading all these reply's are hurting my brain, you guys are to smart.😨😰😓(12 votes)

- what is the biggest decimal number(3 votes)
- There is no biggest decimal number. Real numbers (which include decimals) have no largest number. They are said to extend to infinity. As soon as you find what you think is the largest number, you can add some value to it and get an even larger number.(11 votes)

- Can someone please tell me why regrouping is so important, I did not understand a single thing he said(5 votes)
- This is the answer google gave me: "Regrouping is a great way to make larger calculations easier to do, especially for children. When you're using regrouping with subtraction it can also be known as 'borrowing'. This helpful method is taught in schools to make addition and subtraction easier for students."(5 votes)

- What does arithmetic mean in0:15(6 votes)
- arithmetic is math(1 vote)

- do ten thousandths, hundred thousandths, and millionths exist?(3 votes)
- Yes, they all exist. Also ten-millionths, hundred-millionths, billionths, ten-billionths, hundred-billionths, trillionths, and infinitely many even smaller fractions exist!(4 votes)

- To be honest, i'm just doing these videos for energy points.(4 votes)

## Video transcript

- [Instructor] What we're
going to do in this video is explore place value involving decimals, and in particular, we're gonna think about how you can regroup value
from one place to another, which is gonna be very
useful later in your life when you start doing some
more arithmetic with decimals. So let's first think
about what this number is right over here. So each square represents a one or represents a whole,
so what number is this? Well, you could see that
we have three whole ones, so we could write three, and then we have right over here, a whole is divided into 10
equal bars, these vertical bars, and so each of these are 1/10 and four of them are shaded
in, so it's three ones, 4/10, and in this part right over here, we've divided a whole
into 100 equal sections. It's a 10 by 10 grid, and we can see that one, two, three, four, five, six, seven of them are shaded in. So this represents 7/100, so this is 3.47, or three and 4/10 and 7/100 or three and 47/100. Now what we're going to do
is explore how are other ways you can put the value
into the different places? So let me set up a little table here. I don't think I'm gonna
need all of that space, but we have, in this first example, so we have our ones, we have our ones place, we have our tenths place, and we have our hundredths,
hundredths, hundredths place. I have to curve up a little bit. And so what we just did is we said, hey, this was pretty straightforward. This was three ones, three ones, 4/10, and 7/100, 7/100, but are there other ways
that we could look at it? For example, is there a
way of re-imagining this, so instead of three ones, we have two ones, and we still have 7/100, so how many tenths would we have in order for it to be the same value? Pause this video and think about that. All right, we'll do it
together and to help us, I will put what we had here just now. Now what's different instead
of having three ones, we now have two ones, so we could say that these
are two ones right over here, our two ones. We have our 7/100 right over here. So essentially, we would
have to express all of this in terms of tenths. So how would we express
it all in terms of tenths? Well, this, what used to be a one, this is equivalent to 10/10. Let me make that very clear. I could, let me see if
I could shade this in with that green color, so there you go. I'm gonna shade with the green color and then I'm gonna draw
a bunch of lines here to make it very clear, so I'm just gonna hand draw it so one, two, three, four, five, six, seven, eight, nine, and 10. Did I do that right? One, two, three, four, five,
six, seven, eight, nine, 10. And I didn't draw it
as straight I need to. They really should be 10 equal sections, but it's hand drawn, so
I think you understand. So notice. I took the exact same value, but I have regrouped. I have regrouped this one
right over here into tenths. So how many tenths are here? Well, now I have 10 plus 4/10. So now I have shaded in 14/10. That was interesting. Let's do another example. So now let's imagine another scenario. Let's imagine a scenario where
we have three ones again, but this time, instead of having 7/100, we have 27/100. So in that circumstance, how many tenths would we have? Pause this video and see
if you can work it through. All right, well let's get
that same number again. And now let's think about
how we might have to regroup between the places. So we have our three ones, so that was just like the
first case right over there, so we have our three ones. But now we have 27/100. So in addition to these 7/100, we have to find another 20/100 someplace. Well, the most natural place
to go would be right over here and 20/100 is the same thing as 2/10. So what we want to do is we would convert these
two tenths into hundredths, so let me actually just
shade it in a little bit. So I'm going to convert this
right over here to hundredths. And so did I do that right? One, two, three, four, five,
six, seven, eight, nine, 10. And so there you have it. This plus this gives us our 27/100, and so how many tenths do we have left? We have 2/10, 2/10. So in this situation, we regrouped two from the tenths place and we expressed them as hundredths. So 2/10 became 20/100, added to the 7/100 that you already have and we now have 27/100. Hopefully that makes sense.