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Arithmetic
Course: Arithmetic > Unit 5
Lesson 1: Intro to place value through 1,000Intro to place value
Sal introduces place value using a toy with beads (an abacus). Created by Sal Khan.
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Try to extend the logic of this exercise across number bases other than 10. :) Cool video!(195 votes)
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.(164 votes)
how can one of those be 100(12 votes)
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! :)(27 votes)
Shouldn't there be 9 beads in each row?(0 votes)
At0:28they 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.(19 votes)
- why do we use place value(11 votes)
to help represent numbers, using a base 10 system and to count easier and faster.(13 votes)
- what is the ones place?(8 votes)
- 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.(17 votes)
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?(10 votes)- Calculators can solve much more advanced equations.(11 votes)
What does place value mean?(7 votes)
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.(8 votes)
from which time the abacus was introduced?was it the 17th century or the 18th century?(6 votes)
It was invented in around the 5th century BC(9 votes)
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?(6 votes)
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.(5 votes)
What is the best way to remember multiplication tables?(5 votes)- 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!(7 votes)
0:28Video transcript
Voiceover:Hey Sal. Voiceover:Hello Brit. Voiceover:I picked this up at a garage sale and I know you like colors. Voiceover:I love colors. Voiceover:You wear colorful shirts everyday and I thought you might like this. Voiceover:I do, this is very kind, I like it. So what are you hoping
to do with this thing? Voiceover:Well, at minimum just
maybe represent numbers. Voiceover:To count, keep track of numbers? Voiceover:Counting the number of days or... Voiceover:One, two, three, yeah
I can imagine doing that. Voiceover:Okay, so moving the
beads down is a number, right? Voiceover:Yeah. Voiceover:There's 10. Voiceover:10 there, so maybe that would be 20, 30, 40, 50, 60, 70, 80, 90,100. Yeah, you could count 100
beads to keep track of things. Voiceover:What if I need to count 105 or 106? Do I need to buy another one? I don't even know where I
would get more of these. Voiceover:That would be an
option, maybe not an option if you don't know where to get it. Let's see, well the different
colors, just like we have different forms of
currency, maybe we can have each of these
colors, maybe the columns, they represent a different amount. So this is 10 right over
here, what if we had one of these red beads
represent 10 of these blue beads in the first column. So then, you could go, this would be 10 or you could say that is 10. Voiceover:So there's two
representations of 10 here? Voiceover:Yeah, they way we just
worked it out here, yeah. And then 11 would be that. Voiceover:And this is 21.
Voiceover: 21. Voiceover:Yep, you have two 10s and a one, 21. Voiceover:The wooden colored is going to represent all of the red beads. Voiceover:Yeah, that's a good system. If each column represents 10 of the beads to the column to it's right,
that could be interesting. Because if this represents 10 red beads, that's 10 10s, this is
equivalent to 100 blue beads. And so this would be equivalent to 10 of the brown beads, which would be 100 of the red beads, which would be 1000 of the blue beads, and this would be 10,000 of the blue beads and this would be 100,000 of the other
blue beads, this would be 1,000,000 of the blue beads. Voiceover:So we're going to
be able tor represent all the numbers in between
one and say 1,000,000. Voiceover:I think we can. Voiceover:Let me just give you a number. What about 15,003? Voiceover:So let's think a
little bit about this. So let's try with the big numbers first. So each of these is one,
each of these is 10, each of these is 100,
each of these is 1000. I don't have 15 of these,
but these are 10,000. Each of these are 10,000. So this is one 10,000,
then I could do five 1000s. One, two, three, four,
five, so this is 15,000. So one 10,000, five 1000s, and zero 100s, zero 10s, and then throw a three there. So 15,003.