Early math review
Sal goes through all the numbers from 0 to 100 and shows some interesting patterns. Created by Sal Khan and Arshya Vahabzadeh.
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- At0:39, why does Sal add a new line? Can't he just keep writing the numbers on the same line?(28 votes)
- He did that to show that there is a repeating pattern to the way that numbers are written. He could have continued on the same line, but then it would be more difficult to see the pattern.(3 votes)
- Is there something special about stopping at 100 or can you keep going?(2 votes)
- You can keep going, but things get more complicated. Numbers go into infinity. It goes on like 102, 102, 102, 104, etc.(1 vote)
- Why do we have only 10 different number digits (0,1,2,3,4,5,6,7,8,and 9) ?(2 votes)
- That's a good question! It's a human convention. That means people made it up.
The ten digits we use to write our numerals today is known as a base-10 system of numbers.
If you've ever used tally marks to count, you've used a base-1 system of writing numbers (1 mark for each thing you've counted). They Mayans had a base-5 and base-20 system (http://en.wikipedia.org/wiki/Maya_civilization#Mathematics). Ancient Mesopotamians used a base-60 system. That means they had 60 unique digits! Our modern computers use a base-2 system called binary to calculate data, using only 0 and 1 as digits: (0=0, 1=1, 2=10, 3=11, 4=100, 5=101, 6=110, 7=111, 8=1000, etc.)
It's important to understand that numbers, numerals, and digits are three very different things.
A number is an abstract idea. When we count, we are using numbers to give us an idea of how many of something there is.
When we write that number down, we write a numeral.
And numerals are written by putting different combinations of digits together.
So you can write the same number many different ways! Four (an abstract number, or an idea of how many of something there is) can be written as "4" in the common base-10 system we use for modern mathematics, as "||||" if you were writing in tally marks, as "IV" in Roman Numerals, or as "100" in binary (the base-2 system that computers use).
And they are all the same number! Isn't that amazing?
~ Lauren(3 votes)
- Did most ancient civilizations develop a base 10 number system like us?(22 votes)
- When ancient people began to count, they used their fingers, pebbles, marks on sticks, knots on a rope and other ways to go from one number to the next. As quantities increased, more practical representation systems became necessary.(5 votes)
- Why are numbers 1 through nine? Is there a system of counting based on something other than ten?(10 votes)
- The system of counting today that is most commonly used is the decimal system, with the digits 0 through 9. Because there are 10 different digits, it is said to be a base 10 system. However, there are many other systems with different bases.
For example, the binary system is base 2 and is commonly used in computers. Also, the ancient Sumerians and Babylonians used a base 60 system, which is why we have 60 seconds in a minute and 60 minutes in an hour.
If your parents say it's ok, you can check out this link to read more on this topic: https://en.wikipedia.org/wiki/Radix
Also, this online calculator converts numbers between systems with different bases: https://baseconvert.com/
Hope this helps! If you have any other questions, feel free to ask them in the comment section below!(5 votes)
- can't you only go to 100 on a number grid or is it wrong or right to add 101-120?(5 votes)
- No! It is definitely not wrong to add numbers to the number grid. Number grids are basically infinite, but the normally only go to 100.(3 votes)
- numbers never end like the number 1605,3792 you can go up way more(3 votes)
- amal7o, the number infinite is just a theory. There are yet to be more place values to be added; it would be mathematically impossible. Yes, it can move up but there is only a theory about infinity.(2 votes)
- So each number has a place value like ones,tens, and hundreds. ok So if there is infinite numbers.There's infinite place values. So some where they wold run out of names for place values.So some where out there there is a place value names Allison or unicorn.If there were infinite there would be a place value for every word or name Or is it that there is place values just not named yet?(2 votes)
- There probably are unnamed ones. We just go as high as we need to. Anyways, there is always scientific notation in which can easily go up very high.(4 votes)
- If you already know how to count, can we just skip this video, or do we have to watch it?(2 votes)
- You can certainly skip the video, but it never hurts to review things, and as a bonus, watching the video gives you points and helps towards your badges!(3 votes)
- is there any other pattern rather than the one Sal said?(2 votes)
- You could count by 2's or 5's, but it wouldn't make as nice of a grid. (so the first row would be 0, 2, 4, 6, 8 and the second row would be 10, 12, 14, 16, 18 or the first row would be 0, 5 and the second row would be 10, 15.)(2 votes)
Voiceover: The goal of this video is to essentially write down all the numbers in order from zero to a 100. But I’m going to do it in an interesting way, a way that maybe will allow us to see some patterns in the numbers themselves. So let me just start, so I’m gonna start at zero, one, two, three, four, five, six, seven. eight, and nine, and instead of, of course we know the next number is 10, which I could write down but instead of doing that I’m just going to copy and paste all of this. So copy and paste all of that and see what this does for us. So if I do that, how does that help us? Well we know the next number is 10, which one way to think about it is, it’s a one followed by a zero. What’s the number after that? Well it’s 11, which is a one followed by a one. What’s the number after that? Well it’s a 12, which is a one followed by a two, and then 13, 14, 15, 16, 17, 18, and 19. Well that was pretty neat. This next row of numbers as I went from 10 to 19 looked just like the first ones, so the 2nd number is the same in yellow, but then I added a purple one to the front of it. And one way to think about it is, each of these numbers, the purple one that I added, that represents 10. So 11 could be viewed as 10 plus one, 12 could be viewed as 10 plus two. Let’s see if this keeps working. So let’s take another row of numbers. So let’s take another row , my original row, and what do I get to after 19? Well of course after 19 we get to 20. So 20, two zero and then 21, 22, 23, 24, 25, 26, 27, 28, 29. I think you might start to see the pattern here. What are we gonna do for the next row? Well now we’re in the 30s. So the first number 30 is 30 plus zero, 30 plus one, 30 plus two, 30 plus three which is 33, 34, 35, 36, 37, 38, 39. So just doing that I think you already see the pattern. The number on the right we keep going from zero, one, two, three, four, five, six, seven, eight, nine, and then the number on the left, if we’re between 10 and 19, you’ll always have a one. If you’re between 20 and 29, you’ll always have a two. If you’re between 30 and 39, you’ll always have a three. Now how can I complete this going all the way to 99 pretty fast? Well let’s do that, so that’s going to be my 40s, I haven’t written it out yet. That’s going to be my 50s, this is going to be my 60s, 70s, 80s, and then I have my 90s right over here. And so this one we already said this is going to be my 40s, this is going to be my 50s, this is going to be, I’m trying to make sure I use all my colors, my 60s, this is going to be my 70s, and then I have my 80s, and then of course I have my, let me do a color that, I’ll re-use magenta, I’ll have my 90s. So what if I woulda just take this, so let me just take this right over here, and copy and paste that. So copy, and then let me paste it. So now I have 41, 51, 61, 71, 81, and 91. Now I can do it over here, 42, 52, 62, 72, 82, and 92. And I can do it for each of these, for each of these now. So that’s, now, 44, 54, 64, 74, 84, and 94. And so when I do that we see the full pattern. We see the full pattern and I’m almost done. I’m almost done filling in my numbers from zero to 99. 49, 59,69,79,89,99 and if we just wanna feel good, we could throw in, we could throw in a 100, a 100 right over there. And you’ll see the pattern still holds, we went from one, two, three, four, five, six, seven, eight, nine, and now we got to 10 followed by a zero. That was pretty neat.