manipulation of digits.

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Ryan$

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Hi guys, I've learned when we divide by 10 then we shift the "point" to the left, when we multiply by 10 then we shift it right by one !
my problem is how 3.5*10 = 0.35*100 ? maybe I still not getting the point of shifting right/left ...
here in my example we shifted the point left, then it says we divide the number by 10, so why we multiply 100? I didn't get the trick behind that.


thanks alot!!
 
Okay, suppose we have:

[MATH]N=3.5\cdot10[/MATH]
Now, if we move the decimal point \(n\) places in one direction in one of the factors on the right, then we have to move the decimal point \(n\) places in the opposite direction in another factor. So, if we move the decimal point 1 place to the left in 3.5 (to get 0.35) then we have to move the decimal point 1 place to the right in the 10 (to get 100).

[MATH]N=0.35\cdot100[/MATH]
We have divided one factor by 10 and multiplied the other by 10, essentially multiplying the expression by 10/10 = 1, leaving the actual value unchanged.
 
my problem is how 3.5*10 = 0.35*100 ? maybe I still not getting the point of shifting right/left ...
here in my example we shifted the point left, then it says we divide the number by 10, so why we multiply 100?
Click to expand...
Yes, you have moved the decimal point one place to the left, dividing it by 10 so we must multiply by 10, not 100. And, in what you give, they didn't "multiply 100"- there was already a "10" there. 3.5*10= (0.35*10)*10= 0.35*100.
 
Hi guys if I have 0.0021 and I multiply it by 10 which mean 00.021 .. is it 0.021? if so then why? I really in doubt ! who said that 00 is the same 0?! it's not logically ... !!!

and why for example 56 is the same as 56.0000000 ? who said they are equal? we have point in the second number and in first number we don't have point .. so how they are equal?
 
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What does place value mean?

[MATH]39 \text { MEANS } (3 * 10^1) + (9 * 10^0).[/MATH]
[MATH]39.46 \text { MEANS } (3 * 10^1) + (9 * 10^0) + (4 * 10^{-1}) + (6 * 10^{-2})[/MATH]
[MATH]10 * 0.0021 = 10^1 * (2 * 10^{-3} + 1 * 10^{-4}) = 2 * 10^{-2} + 1 * 10^{-3} = 0.021.[/MATH]
[MATH]56 = 5 * 10^1 + 6 * 10^0 = 5 * 10^1 + 6 * 10^0 + 0 = 5 * 10^1 + 6 * 10^0 + 0 * 10^{-1} = 56.0.[/MATH]
Over and over again you fundamentally ask the exact same question. An equal sign in math MEANS that two superficially different expressions have the SAME NUMERIC value. And you keep saying that is not logical! The meaning assigned to symbols is arbitrary and is a matter of social agreement. We could call dogs cats and cats dogs without any logical difficulty whatsoever, but, if you think "dog" means "cat," you are not going to understand people who speak English.

So long as you keep saying things like 56 looks different from 56.0 and so 56 = 56.0 is not true, you can forget about learning anything about math. You have now asked pretty much the same question 288 times and received the same answer. If you refuse out of stupidity or stubbornness to learn what the symbols in math mean, you will remain mathematically ignorant.
 
Two things:
1) Multiplication Works.
2) Read up on "Significant Figures"
 
Ryan$ said:
Hi guys if I have 0.0021 and I multiply it by 10 which mean 00.021 .. is it 0.021? if so then why? I really in doubt ! who said that 00 is the same 0?! it's not logically ... !!!

and why for example 56 is the same as 56.0000000 ? who said they are equal? we have point in the second number and in first number we don't have point .. so how they are equal?
Click to expand...
Nobody said THAT or THAT!!
 
The numeral "00" means 0x10+ 0x1= 0. The numeral "0" means 0x1= 0. They are two different numerals representing the same number.
 
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