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Lesson 1: Numbers 0 to 120

Number grid

Sal goes through all the numbers from 0 to 100 and shows some interesting patterns. Created by Sal Khan and Arshya Vahabzadeh.

Want to join the conversation?

• At , why does Sal add a new line? Can't he just keep writing the numbers on the same line?
• He made a number grid,not a number line.
• Why do we have only 10 different number digits (0,1,2,3,4,5,6,7,8,and 9) ?
• 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
• Is there something special about stopping at 100 or can you keep going?
• You can keep going, but things get more complicated. Numbers go into infinity. It goes on like 102, 102, 102, 104, etc.
• Did most ancient civilizations develop a base 10 number system like us?
• 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.
• Why are numbers 1 through nine? Is there a system of counting based on something other than ten?
• 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.

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!
• can't you only go to 100 on a number grid or is it wrong or right to add 101-120?
• 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.
(1 vote)
• What comes after 100 since its the last number?
(1 vote)
• 101 comes next because 100 is actually not the last number. Numbers go all the way up to infinity, which would take FOREVER to count!
• 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?
(1 vote)
• 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.