Positional value

I don't understand what you are saying. What does "facing 9" mean? What does "I am end with units system right" mean?

Do you see that when you count the tenth bean, you have filled a cup, so that you go from 09 (no full cups, 9 free beans) to 10 (1 full cup, 0 free beans)? The reason we don't need digits greater than 9 is that once you pass 9, you fill a cup and reset the number of free beans. What would have been 10 beans becomes 1 cup.
 
The reason we don't need digits greater than 9 is that once you pass 9, you fill a cup and reset the number of free beans.

how will u convert the upper line into real life decimal system process of counting without the analogy of beans...

once we use 9 when counting then we place zero in place of 9 in unit place and place 1 in tens place to make it 10.
but still why we place zero removing 9 as we know after 9 10 comes thats why or we dont have any more decimal digits thats why we go back to the first digt that is zero... ok then how we bring 1 to the tens place.... ok now we decided that there should be a tens place also so 1 in tens place and 0 in units place???
 
Saumyojit said:
The reason we don't need digits greater than 9 is that once you pass 9, you fill a cup and reset the number of free beans.

how will u convert the upper line into real life decimal system process of counting without the analogy of beans...

once we use 9 when counting then we place zero in place of 9 in unit place and place 1 in tens place to make it 10.
but still why we place zero removing 9 as we know after 9 10 comes thats why or we dont have any more decimal digits thats why we go back to the first digt that is zero... ok then how we bring 1 to the tens place.... ok now we decided that there should be a tens place also so 1 in tens place and 0 in units place???
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Have you never counted? You should be doing this all the time (without beans). I used beans because you appear never to have been taught the basics.

1
2
3
4
5
6
7
8
9

Now the next number will be ten. It is big enough that we can start counting tens: we have 1 of them. But we have 1 ten and 0 ones, because all of our units are included in the single ten. This is often called "regrouping"; ten ones is the same as one ten. So the next number is

10 = 1 ten and 0 ones

We continue, adding ones:

11
12
13
14
15
16
17
18
19

Now if we increase the ones to ten, we can group those together and instead make another ten. So now we have 2 tens, but there are no additional ones. So the next number is

20

Have you really never been taught this?

One more point: You could say that we change after 9 is that we have no more digits to use; but the reason for that is that we don't need to, because we have a tens place to use. We want to be as efficient as possible, so we use what is available. As soon as you are able to add to the tens place, you do.
 
ok and how 10 ^ index concept came and why we are merging base 10 with the index and then multiplying with each digit ....
why base 10? as it has everytime 10 digits possibility for each position?
 
Please ask each of these questions using more words so we can be sure what you mean.

What do you mean by "10^index concept"?

What do you mean by "merging base 10 with the index"?

Why base 10? I think we've told you that: It's an arbitrary choice, influenced by having 10 fingers. What more do you want?
 
Dr.Peterson said:
Please ask each of these questions using more words so we can be sure what you mean.

What do you mean by "10^index concept"?

What do you mean by "merging base 10 with the index"?

Why base 10? I think we've told you that: It's an arbitrary choice, influenced by having 10 fingers. What more do you want?
Click to expand...

324=3*10^2+2*10^1+4*10^0

the digit is getting multiplied with 10 ^ zero ,1 ,2 ..how this form came or logic behind 10 ^0,1,2
 
Do you mean, "Why are 10^0, 10^1, 10^2 equal to 1, 10, 100 respectively?"

What is your understanding of the meaning of powers? What parts of this can you answer for yourself?

I need to see you doing some thinking for yourself, rather than asking questions we can't seem to answer for you.
 
We decided on using a base 10 system. This means that when we reach 10 in any one position it equals and becomes 1 in the position to the left.
 
Dr.Peterson said:
Do you mean, "Why are 10^0, 10^1, 10^2 equal to 1, 10, 100 respectively?"

What is your understanding of the meaning of powers? What parts of this can you answer for yourself?

I need to see you doing some thinking for yourself, rather than asking questions we can't seem to answer for you.
Click to expand...
i know 10^0=1
10^1=10
10^2=100

why we multiply this with each digit in expanding form
 
Because each place is worth 10 times as much as the one to its right. The rightmost is worth 1, the next 10, the next 100. Is that not clear?
 
@Dr.Peterson

54 means= 4 means 4 ones and 5 is 5 tens

But still
54 can also mean 50 ones and 4 ones =50*10^0+4*10^0

then again as u told we represent 50=5 tens's and zero ones "regrouping"
5*10^1 +4*10^0

Now my question is : who has decided that whenever 10 ones happen we will regroup it to 1 ten?
 
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Dr.Peterson said:
Why powers of ten? Because that's as far as you can count on your fingers, and because it's not too small and not too large. The number 34 can be shown as 3 pairs of hands and 4 more fingers.
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I did not understand this line.34 is expressen as 3 pairs means 60 fingers and 4 fingers .

Why the analogy of hands even coming in decimal.

see my logic is that we use 10 as a base as we have 10 unique digits (0-9)

where is wrong with my logic??
or

Because each place is worth 10 times as much as the one to its right. The rightmost is worth 1, the next 10, the next 100
thats why we can see there is progression of 10 to the power series
 
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Saumyojit said:
Now my question is : who has decided that whenever 10 ones happen we will regroup it to 1 ten?
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That doesn't really matter, does it? We don't know the individual who invented most ideas in mathematics.

But I already mentioned the answer here:
Dr.Peterson said:
... I imagine it took Europeans some time to get used to the idea when place value was introduced (from India by way of the Middle East), but they soon saw its value, even if they didn't quite see why. And, of course, it was only later that it was commonly expressed in terms of powers of ten, as exponents hadn't quite been invented yet, and most people wouldn't understand 10^0. But that was all hidden in the concept.
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You can easily find more details. See, for example, https://en.wikipedia.org/wiki/Positional_notation
 
Saumyojit said:
I did not understand this line.34 is expressen as 3 pairs means 60 fingers and 4 fingers .

Why the analogy of hands even coming in decimal.

see my logic is that we use 10 as a base as we have 10 unique digits (0-9)

where is wrong with my logic??
or

Because each place is worth 10 times as much as the one to its right. The rightmost is worth 1, the next 10, the next 100
thats why we can see there is progression of 10 to the power series
Click to expand...
We didn't already have the "digits" 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 until positional notation created a need for them.

But are you aware that the word "digit" originally meant "finger"? The basic reason for using base 10 is that we have 10 fingers.

As for "pairs of hands", don't you realize that two hands contain 10 fingers? So 3 pairs of hands contain 30, not 60.
 
what shall the base of octal be ?
my hand has 10 fingers should i make it 10 then?
 
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