Math 5: Place Value

5th GradeMath
Elementary and Middle School5th Grade
LanguageEnglish Language

Transcript

00:25

And with just those ten digits, we're able to represent numbers way bigger than just

00:30

ten.

00:31

Which is definitely a good thing…you wouldn't want your paycheck to say "$9…plus some [Picture of a pay check]

00:35

more, we guess."

00:36

And it's all thanks to the magic of place values.

00:39

The idea of place values is pretty simple.

00:41

We count up from zero using our regular digits, but once we run out, aka once we get to 9, [Scoreboard counting up]

00:46

we tack on a new place value.

00:48

So if we have 9, and we want to go up by one, we replace the 9 with a 0, and put a 1 to

00:53

the left.

00:54

The 0 is holding the ones place value…

00:56

…while the 1 is holding the tens place value. [Arrows pointing to the place values]

00:59

And since saying, "8, 9, 1 in the tens place value and zero in the ones place value," gets

01:04

kinda clunky, we just call it "ten." [Long description gets crossed out]

01:06

Without place values, we'd need new symbols for each new number, and if you think math

01:11

is hard now, try doing it when you need to remember millions of different, tiny symbols. [Random symbols appear and girl runs away]

01:15

Calculators would need to be the size of huge playgrounds. [Girl jumping on a big calculator]

01:18

Boring, mathy playgrounds.

01:20

The place values are all organized around powers of ten. [Coop pointing to a blackboard]

01:23

Each time we add a new place value to the left, we're multiplying the last one by ten.

01:27

We start with ones…

01:29

…then multiply that by ten to get tens…

01:32

…then multiply that by ten to get to the hundreds…

01:34

…then multiply that by ten to get to the thousands…

01:37

…then, well, we think you get the idea.

01:39

We could keep doing this for a really, really long time.

01:43

However, let's not…we don't want this video to never end, we have lunch plans. [Guy apologies for being late to lunch]

01:47

These place values give us a very simple way to understand what's going into our numbers.

01:51

Take 2,074, for example.

01:54

In the ones place, we see a 4.

01:56

So 2,074 definitely contains 4.

01:59

When we move over to the tens, we see a 7, so 2,074 also contains 7 times 10, aka 70. [Each component of the number is highlighted]

02:06

Next, when we look at the hundreds we see a 0.

02:09

Sorry, 2,074, but that means you contain 0 times 100, or a big, fat 0.

02:15

But no need to despair.

02:17

In the thousands we see a two, so 2,074 also contains 2 times 1,000 which is 2,000.

02:23

And, surprise surprise, if we add up those four numbers, we get—drumroll—2,074.

02:30

Which is a much nicer number to see on a pay check. [Paycheck with $2,074 on it]

02:32

And if you're ever confused about what a certain place value represents, just look for the [Boy holding a teddybear looks confused]

02:36

decimal point. [Arrow pointing to the decimal point on a price tag]

02:37

It always sits just to the right of the ones, which is a pretty cozy spot if you ask us.

02:41

So if you have $26,000, that's enough money to buy a pretty good speedboat… [ATM showing $26,000]

02:46

…but if that decimal point hops four places to the left, you're down to $2.60…

02:50

…which is only enough to buy a pretty blah sandwich. [ATM showing $2.60]

02:53

And we definitely wouldn't recommend taking it out on the lake for a spin. [Woman stood on a sandwich in the lake sinks]