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• Hi, I’m Rob. Welcome to Math Antics.

• In this lesson, were going to learn how our basic number system works

• and were going to learn about an important concept called Place Value.

• The number system that we use in math is calledbase 10’, because is uses ten different symbols for counting.

• Math could use other systems that are based on a different number (likebase 2’ orbase 8’),

• but I’ll give you ten guesses as to why the number ten is such a popular choice.

• The ten symbols that we use are calleddigitsand they look like this:

• zero, one, two, three, four, five, six, seven, eight and nine.

• At first glance, you might think that’s only nine digits, but remember,

• the zero counts as one of the digits also.

• To see how our numbers system uses these digits to represent amounts,

• let’s pretend that we have an apple orchard full of apple trees,

• and each of these trees is loaded with big, juicy, red apples

• that we need to pick and then count for our records.

• [crunch]

• Were going to use something called a ‘number placeto count.

• The best way to understand a number place is to imagine that it’s like a small box

• that’s only big enough to hold one digit at a time.

• As we count, well change the digit that’s in the number place to match how many apples weve picked.

• For example, if we start with no apples at all, we put the digit ‘0’ in the number place because zero meansnone’.

• But then, as the apples start coming in from the orchard, we begin to count

• one, two, three, four, five, six, seven, eight and nine.

• Okay, now weve got nine apples, but weve also got a problem.

• Weve already run out of digits to count with.

• The highest digit we have is a ‘9’, but there are a LOT more apples left to count.

• What will we do?

• The solution is to use groups to help us count.

• If we pick just one more apple, well have ten, right?

• So let’s combine those ten apples into a single group.

• Sohow many apples do we have? Ten!

• BUThow many GROUPS of ten apples do we have? Ahjust ONE!

• Does that help us with our lack of digits problem?

• It sure does, IF we use another number place!

• Instead of using this new number place to count up individual apples

• one at a time like we did with the first number place.

• Were going to use it to count apples TEN at a time.

• In other words, well use it to keep track of how many groups of ten apples that weve picked.

• For example, if weve picked only one group of ten, then well put the digit ‘1’ in that number place.

• If weve picked two groups of ten, then well put the digit ‘2’ in that number place,

• and if weve picked three groups of ten, then well put the digit ‘3’ in that number place. And so on.

• Do you see what’s happening?

• Because the new number place is being used to count GROUPS of ten,

• it’s allowing us to re-use our original ten digits, but this time they are able to count (or represent) bigger amounts.

• Since this new number place is for counting groups of ten, were going to name itthe tens place’.

• And well name our original number place, ‘the ones placebecause we used it to count things one at a time.

• And here’s the really important thingwere not going to use the new number place instead of the old one

• were going to use it along side of the old one so that we have one number place for counting by ones

• and another number place for counting by tens.

• Using these two number places together lets us represent amounts that are in-between the groups of ten.

• For example, if weve already picked thirty apples, then there will be a ‘3’ in the tens place

• because we have three groups of ten.

• But there will be a ‘0’ in the ones place, because there are no individual apples left over.

• Butif we have picked thirty-two apples, then there will be a ‘3’ in the tens place

• and a ‘2’ in the ones place to represent the two individual apples that are not in the groups of ten.

• In fact, using only our ten digits and these two number places, we can count all the way from zero up to ninety-nine.

• At ninety-nine, both of our number places are maxed out with the highest digits and we won’t be able to count any higher,

• UNLESS... we get another number place!

• If weve picked ninety-nine apples and then we pick just one more, well have exactly one-hundred apples.

• And if we make a group from those one-hundred apples,

• we can use this new number place to count how many groups of one-hundred weve picked.

• That means that we can re-use the same ten digits AGAIN in this new number place to count how many groups of one-hundred we have.

• And you guessed itit’s calledthe hundreds placebecause we use it to count groups of a hundred.

• Are you starting to see how ourbase 10’ number system works?

• It uses different number places to represent the different sized groups that we use to count.

• And the digits in those number places tell us how many of each group we have.

• The digit in the ones place tells us how many ones we have.

• The digit in the tens place tells us how many groups of ten we have.

• And the digit in the hundreds place tells us how many groups of one-hundred we have.

• And have you noticed that each time we got a new number place to count larger groups,

• we placed it to the LEFT of the previous number place.

• That’s important because number places are always arranged in the exact same order.

• Starting with the ones place, as you move to the left, the number places represent larger and larger amounts.

• And did you also noticed that each new number place represents groups that are

• exactly ten times bigger than the previous number place?

• Ten is ten times bigger than one and one-hundred is ten times bigger than ten.

• That’s really important because it helps us see the pattern for bigger number places.

• It helps us to see that the next number place will count groups of ten times one-hundred, which is one-thousand.

• That’s why it’s calledthe thousands place’.

• And the next number place will count groups ten times bigger than that! It’s the ten-thousands place!

• And the number places keep on going like that.

• Next is the hundred-thousands place.

• Thenthe millions place.

• Thenten-millions.

• Thenone-hundred-millions.

• Thenbillions! And so on

• Oh, and you may notice that when we get a lot of number places next to each other like this,

• it’s a little hard to quickly recognize which place is which.

• That’s why many countries use some kind of separator every three places to make them easier to keep track of.

• For example, in the U.S. we use a comma every three number places to make it easier

• to identify things like the thousands place, or the millions place.

• Seeing all these number places together helps you understand what we mean byplace value’.

• In a multi-digit number, the number PLACE that a digit is in, determines it’s VALUE.

• Even though we only have ten digits, each digit can stand for different amounts depending on the place that it occupies.

• If the digit ‘5’ is in the ones place, it just means five.

• But, if a ‘5’ is in the tens place, then it means fifty,

• and if a ‘5’ is in the hundreds place, it means five-hundred.

• And it’s the same for bigger number places.

• A ‘5’ in the hundred-thousands place means five-hundred-thousand,

• and a ‘5’ in the billions place means five-billion!

• See how a digit’s place effects its value?

• Of course, when we work with numbers in math, most of the time the number places are invisible.

• But the underlying pattern is always the same.

• Oh, and because the number places are invisible, in certain cases

• youll need to use zeros to make it clear what number youre talking about.

• To see what I mean, imagine that this ‘5’ is in the hundreds place to represent five-hundred,

• but if you make the number places invisible, then it just looks like five and not five-hundred.

• Soto make sure people know you mean FIVE-HUNDRED, you need a ‘5’ in the hundreds place,

• a ‘0’ in the tens place,

• and a ‘0’ in the ones place.

• Now you can tell that the ‘5’ is in the hundreds place and it means five-hundred.

• Okaynow a great way to see place value in action with some actual numbers is to expand them

• to show that theyre really combinations of different groups.

• When we do this, it’s called writing a number inExpanded Form’.

• For example, we can expand 324 to be 300, 20 and 4,

• because the ‘3’ is in the hundreds place and means three-hundred,

• the ‘2’ is in the tens place and means twenty,

• and the ‘4’ is in the ones place so it just means four.

• So 324 in expanded form is the combination of those amounts:

• three-hundred plus twenty plus four.

• Let’s try writing another number in expanded form: 6,715

• We can expand this into

• six-thousand, (because the ‘6’ is in the thousands place)

• plus seven-hundred, (because the ‘7’ is in the hundreds place)

• plus ten, (because the ‘1’ is in the tens place)

• and five, (because the ‘5’ is in the ones place)

• So the expanded form is six-thousand plus seven-hundred plus ten plus five.

• Alrightso do you see how ourbase 10’ number system works?

• Number places are used to count different sized groups.

• Each group is ten times bigger than the next,

• and the digits in the number places tell us how many of each group we have.

• The tricky part is that the number places are invisible,

• so you have to know how they work behind the scenes in order to make sense of multi-digit numbers.

• How do you like them apples?

• The exercises for this section will help you practice so that you get used to how place value works,

• which is super important if you want to be successful in math.

• As always, thanks for watching Math Antics and I’ll see ya next time.

• [Clank!]

• That gives me an idea...!

• ...I could make pies out of these!!

Hi, I’m Rob. Welcome to Math Antics.

A2 初級

# 数学アンチックス - 位相値 (Math Antics - Place Value)

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Yassion Liu に公開 2021 年 01 月 14 日