How decimal division is explain in real life?

[CollinsArg]

Okay, hello there! I'm just beginning with an electricity course, and I saw this formula to claculate the Vrms :

" Vrms=Vp/√2"... I'm trying to understand the origen of this formula, I see that I have to divide Vp%1,4142... but how do you explain a division with a decimal number..I mean If I divide 4apples into 2 I would have 2 groups of 2 apls. that's 2 as answer, but how can I divide 4 apples into 1,41? is there another way to explain this division?. Thanks.

 

[andrewkirk]

Apples are in general only dealt with by integers, which is discrete maths/arithmetic. To understand dividing by 1.41 we need a different analogy, because that's continuous maths/arithmetic. Here's one.

I walked across a large town square using a steady, regular pace. The courtyard is paved with square flagstones. By experimenting with single paces I worked out that my average pace has the length of about 1.41 flagstones. If it takes me 500 paces to get from one side of the square to the other, approximately how many flagstones would there be along an edge of the square?

 

[Mark44]

Okay, hello there! I'm just beginning with an electricity course, and I saw this formula to claculate the Vrms :

" Vrms=Vp/√2"... I'm trying to understand the origen of this formula, I see that I have to divide Vp%1,4142... but how do you explain a division with a decimal number..I mean If I divide 4apples into 2 I would have 2 groups of 2 apls. that's 2 as answer, but how can I divide 4 apples into 1,41? is there another way to explain this division?. Thanks.

Division of 4 by 1.4142 is exactly the same as dividing 40000 by 14142. Just by rough estimate I can see that 14142 will go into 40000 somewhere between 2 and 3 times.

Did you ever learn long division in school?

 

[axmls]

The "dividing apples" analogy definitely falls apart when using an irrational number. Let's not even talk division here. Do you have a problem with the fact that we can't represent $\sqrt{2}$ as a fraction? This, if you're having trouble with dividing by it, would be just as disconcerting if you ask me.

 

[abecedarian]

With the apples, 1.4142 means you have 1 whole apple and 4142 pieces of another that was cut into 10000 equal sized pieces.

If you multiply both sides by 10 to some power so as to eliminate the decimal point in the equation... for instance:

4 / 1.4142 (original)
40 / 14.142 (* 10 on each side (10^1))
400 / 141.42 (* 100 on each side (10^2))
4000 / 1414.2 (* 1000 on each side (10^3))
40000 / 14142 (* 10000 on each side (10^4))

All equal the same: 2.8285 (rounded to 4 decimal places).

 

[meBigGuy]

1. That RMS formula only holds for a sine wave. It represents the voltage which when applied to a load, will dissipate the same power as the sinewave.
You can read about its derivation in many places (rms of a sine wave). But, I understand that is not your question.

2. If you had 5 volts and divided it by 1.1 you world have 4.54545454... volts. You can do that with resistors. why is that a problem?
You don't always have to divide by integers. You can divide by anything (except 0)

Your example with apples is different since it is hard to conceive of 1.41 groups. But, you can do it, and there is a valid answer.
If you divided 4 apples into 1.4 groups, you would have 2.86 apples per group. 0.4 of a group would have 1.14 apples, and 1 group would have 2.86 apples.
Mathematically it works, even though it does not seem logical to think of 0.4 groups.

 

[symbolipoint]

A person learning the basic properties of numbers, like in Algebra 1, can use those properties. If you really feel uncomfortable about an irrational denominator, you can rationalize by multiplying the entire "fraction" by 1. If the value is truly irrational, then you approximate. Doing by long-hand, you also multiply all the fraction by 1 so that your divisor is a whole value (which may be an approximation itself, sometimes).

 

[CollinsArg]

With the apples, 1.4142 means you have 1 whole apple and 4142 pieces of another that was cut into 10000 equal sized pieces.

If you multiply both sides by 10 to some power so as to eliminate the decimal point in the equation... for instance:

4 / 1.4142 (original)
40 / 14.142 (* 10 on each side (10^1))
400 / 141.42 (* 100 on each side (10^2))
4000 / 1414.2 (* 1000 on each side (10^3))
40000 / 14142 (* 10000 on each side (10^4))

All equal the same: 2.8285 (rounded to 4 decimal places).

Thanks! I think I get it =)

 

[abecedarian]

Thanks! I think I get it =)

Cool!

I, as well as a lot of people, do a little shorthand to get around decimals whenever possible. Also makes it handy when we have to show our work, like how we get from one step to the next but can use calculators. Count decimal places on the side of the operation you want to get rid of the decimal, and ...
Vrms = 4 / 1.4142
Vrms = (4 * 10000) / (1.4142 * 10000)
Vrms = 40000 / 14142
Vrms = 2.8285

But, you could've just worked out:

       _________
1.4142 ) 4.0000

*notice there are the same number of decimal places on both sides, just one is filled with zeroes?

 

[russ_watters]

...I mean If I divide 4apples into 2 I would have 2 groups of 2 apls. that's 2 as answer, but how can I divide 4 apples into 1,41?

Sure you can. The RMS is a special type of average. If yesterday you had 4 apples and today you have 2, that's an average of 2 apples. But if yesterday you had 4 and today you have 3, that's an average of 3.5, even if you never actually had half an apple. But for certain complex functions (like sine waves), the average is computed differently. That's what RMS is for.

 

[sophiecentaur]

RMS is an indication of the actual Power being transferred. At any instant, the Power will be V(t)²/R and averaging this will give you the average power. The equivalent DC voltage V_dc would transfer the same amount of power.
All sinusoids have the same relationship between the peak value and the RMS value. If you take a square wave, symmetrical about 0V), the RMS value is exactly the same as the Peak value. If you have a complicated waveform the only ways to measure the Power are to find the actual heating effect (the only way for high frequency signals) or by sampling the waveform and integrating the V²s for each sample

 

[CWatters]

how can I divide 4 apples into 1,41?

Perhaps your problem that you see "apples" as entities that can't be "cut up" into smaller units? There is no problem spreading 4 Liters of paint over 1.41 square meters of wall (if you put it on thick enough).

 

[sophiecentaur]

but how can I divide 4 apples into 1,41?

I just read this again and it made me think. Dividing integers by integers when the answer is an integer is the only time that the word "sharing" is really applicable. It's what we started the fourth arithmetical sign / operation with in primary school. Dividing (non prime) integers by anything else than one of its factors is a big leap and can give a decimal result that recurs for ever but the answer is still a Rational Number and expressible in a finite number of digits (xyz/abc ). Dividing 4 litres rather than 4 apples is another step because 1l is a Real variable (1.000000l +/- the accuracy of measurement). The answer is still rational but what about when you divide something by √2? That's an irrational number answer and dividing by π? That's a pretty common sum that we do in wave calculations and gives a transcendental answer.
Numbers can be fun on their own.

 

[fresh_42]

That's a pretty common sum that we do in wave calculations and gives a transcendental answer.

That reminds me on the fact that we all live / calculate / model or whatever in algebraic closed sets and therefore null sets.

 

[andrewkirk]

That reminds me on the fact that we all live / calculate / model or whatever in algebraic closed sets and therefore null sets.

What is an 'algebraic closed set'? Is that referring to topological closure or closure under addition, subtraction and multiplication, or something else? If the meaning is topological then it doesn't work, as [0,1] is topologically closed and not null.

 

[fresh_42]

What is an 'algebraic closed set'? Is that referring to topological closure or closure under addition, subtraction and multiplication, or something else? If the meaning is topological then it doesn't work, as [0,1] is topologically closed and not null.

Yes, in a very strict way you are right. Algebraic closed sets are basically those which can be described by equations. $GL(n) ⊂ M(n)$ is open (and dense), its complement {$A ∈ M(n) | det(A) = 0$} closed. Of course we deal with regular matrices and other open sets. My remark was more informally meant since we handle a world of equations whereas "most" in it is unequal, not smooth and not differentiable.
However, I like to say that I'm driving my car in $C^∞$.

 

[mathexam]

In real life, computations are not always precise. Some times, as in electronics, actually many times, you will have to deal with irrational numbers. Physics in general, especially at the atomic level, will not always deal with whole numbers.