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# Intro to place value

Sal introduces place value using a toy with beads (an abacus).  Created by Sal Khan.

## Want to join the conversation?

• Try to extend the logic of this exercise across number bases other than 10. :) Cool video!
• Unary-----------1 for every number.
1
11
111
1111
11111
Thats good for learning to count but not really anything else
Binary----------1 for every power of 2 in other words 2 beads per row
1
10(this is 2 not 1)
11
100
101
Powers do go up fast but powers of 2 are the slowest
Ternary---------1 for every power of 3 or 3 beads per row
1
2
10(3 not 2)
11
12
Quarternary---------1 for every power of 4
Twice as efficeint as binary to express the same thing
Quinary----------1 for every power of 5
and we could go on to base 360 but 360 is a lot of beads.
You know the babylonians used base 60. I find that really interesting. Time in hours:minutes:seconds is also base 60.
• how can one of those be 100
• It just represents the number 100. Because you don't have enough beads to count to numbers that are higher than 100 you have to use one of the beads to represent it. It's kind of like money. Let's say you have a 100 dollar bill, that represents 100 of the 1 dollar bills. You are not actually carrying around 100 different bills, you don't need to because the 100 dollar bill represents that amount, same as the one bead in the video represents 100 beads. I hope that this will help you to understand it a bit better! :)
• Shouldn't there be 9 beads in each row?
• At they say that there is ten beads in each row.
They did it because it is easy to find multiples of 10 and the numbers are easy to deal with.
• why do we use place value
• to help represent numbers, using a base 10 system and to count easier and faster.
• what is the ones place?
• The ones place is the first number before a decimal. The numbers could be 1,2,3,4,5,6,7,8,9 or 0. In the number 235, the number 5 is in the ones place. In 14,567, 7 is the number in the ones place.
• Three questions about the abacus:
1) Are they still used?
2) Did China only use them or did they spread to other countries?
3) What made people switch over to modern calculators?
• Calculators can solve much more advanced equations.
• What does place value mean?
• It means the value of the individual number given by its placement in any number. For example, tens place value means that any number in that placement, say the 5 in 57, is worth 10 each. So, in 57, 5 is worth 5 tens, or 50.
• from which time the abacus was introduced?was it the 17th century or the 18th century?
• It was invented in around the 5th century BC
• Is there such a thing as an abacus for bases other than 10?
Like, I know you can just take one and say, "These are powers of two now", but I mean, is there a more intuitive sort of way to represent it physically?
• a series of objects with boolean on/off states would work as a binary abacus. For example, a row of on/off switches would work since each switch could count as a 1 or a 0.
• What is the best way to remember multiplication tables?
• There are many way to master your multiplication tables. Practice does make permanent. The more you practice, the better you will remember them. Here are a couple of tricks to help you.

Remember that every multiplication problem has a twin (2 x 3 = 3 x 2)

2~ add the number by itself
example 2 x 9 = 9+9

5~ the last digit in the answer will always be 0 or 5

6~ when you times an even number by 6, they will both end in the same digit
Example; 6 x 6 = 36 6 x 4 =24 6 x 2 = 12

9~ The answer is always 10 times the number minus the number
Example 9 x 6 = 60 60 - 6 = 54 9 x 6 = 54

10~ put a zero after it
Example 8 x 10 = 80 5 x 10 = 50

Keep practicing and these answers will become a permanent part of your math memory!