How to determine 'even number' or 'odd number' in the significant figure?

Indranil

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Two numbers 3.8 and 0.125. If I multiply, I get (3.8). (0.125) = 0.475. As the least number digit (3.8) is in two significant figures, so the answer should be in two significant digits. So the question is what would be the digits 1) 0.47 or 2) 0.48? How to determine 'the even number' and 'the odd number' if I round it off?
 
Two numbers 3.8 and 0.125. If I multiply, I get (3.8). (0.125) = 0.475. As the least number digit (3.8) is in two significant figures, so the answer should be in two significant digits. So the question is what would be the digits 1) 0.47 or 2) 0.48? How to determine 'the even number' and 'the odd number' if I round it off?

Both 0.47 and 0.48 are the same distance from 0.475, so the choice of "nearest hundredth" is arbitrary.

Are you saying that you have been taught in this case to round to the even digit? That would be 0.48. But that rule is not universal; it is just one possible convention.
 
Both 0.47 and 0.48 are the same distance from 0.475, so the choice of "nearest hundredth" is arbitrary.

Are you saying that you have been taught in this case to round to the even digit? That would be 0.48. But that rule is not universal; it is just one possible convention.
Could you please simplify the point "nearest hundredth is arbitrary''?
 
You haven't told us whether you're using any particular set of rounding rules. There are different sets of rounding rules for significant figures. Some people use one set of rules; other people use different rules. Do you have a particular set of rounding rules?




I'm getting a 500 Infernal Server error when I submit this post, so I'll try putting the rest of it in another post.
 
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Continuing …

If you are not using a set of rounding rules, then it doesn't matter whether you choose 0.47 or 0.48 because each of those numbers is a hundreth unit and neither of them is closer to 0.475 than the other (because 0.475 is located halfway between them). So, there is no single "nearest" hundreth unit to 0.475 -- there are two of them. You may pick either one.
 
Finishing …

In math, when we need to make a choice from a set of choices and it doesn't matter how we choose, then we say the choice is 'arbitrary'.
 
Could you please simplify the point "nearest hundredth is arbitrary''?

It's the choice, not the hundredth, that I said is arbitrary!

There are two numbers that are both "the nearest multiple of 0.01 to 0.475", because both 0.47 and 0.48 are 0.005 away from it. So we could choose to round to either of those, and we would be correct. That is called an arbitrary choice. It doesn't matter which. (Perhaps you should look up the word "arbitrary" in a dictionary.)

There are various rules that have been made up for doing this; since you asked about odd and even, you probably have been taught to round to whichever of the two nearest numbers ends in an even digit, which in this case would be 0.48. But that rule is arbitrary, in the sense that it would make no mathematical difference whether we take that rule or another. (There are reasons to choose one rule over another, such as to avoid some sort of statistical bias, like always rounding up; but that still doesn't make a different choice wrong.)
 
It's the choice, not the hundredth, that I said is arbitrary!

There are two numbers that are both "the nearest multiple of 0.01 to 0.475" because both 0.47 and 0.48 are 0.005 away from it. So we could choose to round to either of those, and we would be correct. That is called an arbitrary choice. It doesn't matter which. (Perhaps you should look up the word "arbitrary" in a dictionary.)

There are various rules that have been made up for doing this; since you asked about odd and even, you probably have been taught to round to whichever of the two nearest numbers ends in an even digit, which in this case would be 0.48. But that rule is arbitrary, in the sense that it would make no mathematical difference whether we take that rule or another. (There are reasons to choose one rule over another, such as to avoid some sort of statistical bias, like always rounding up; but that still doesn't make a different choice wrong.)
I don't understand the point 'There are two numbers that are both "the nearest multiple of 0.01 to 0.475", because both 0.47 and 0.48 are 0.005 away from it'. Could you simplify the point, please?
 
I don't understand the point 'There are two numbers that are both "the nearest multiple of 0.01 to 0.475", because both 0.47 and 0.48 are 0.005 away from it'. Could you simplify the point, please?

Please state what you think I mean, or what you think I should be saying, so I can correct your misunderstanding.

I think I have made it about as clear as I can, apart from language issues, which I can't predict. It's not just a matter of simplifying (using fewer or easier words?), but of knowing how you, the reader, will interpret what I say. The way to communicate clearly in such circumstances is to dialogue until we understand each other. Just having me restate it without knowing why doesn't help. (It hasn't yet!)
 
I don't understand the point 'There are two numbers that are both "the nearest multiple of 0.01 to 0.475", because both 0.47 and 0.48 are 0.005 away from it'. Could you simplify the point, please?

I'll make one more attempt to restate this, before getting feedback from you.

You want to round 0.475 to two significant digits, which means to the nearest hundredth. Right?

This means that you want to find the closest number to 0.475 that is a multiple of 1/100 = 0.01. Right?

There are two numbers near 0.475 that are multiples of 0.01, namely 0.47 and 0.48. Right?

Each of these differs from 0.475 by 0.005: 0.475 - 0.47 = 0.005, and 0.48 - 0.475 = 0.005. Right?

So these are the same distance from 0.475, and either could be considered to be "the nearest multiple of 0.01 to 0.475", just as two towns that are each 5 kilometers from you could both be called "the nearest town" (or neither could).

Since you need one answer, you can either choose one randomly (arbitrarily), or follow an arbitrary rule that tells us which to choose (such as the rule you have evidently been taught, to use the one whose last digit is even).

Is this longer version clearer? If not, tell me where you are unsure what I mean, or where you disagree.
 
I'll make one more attempt to restate this, before getting feedback from you.

You want to round 0.475 to two significant digits, which means to the nearest hundredth. Right?

This means that you want to find the closest number to 0.475 that is a multiple of 1/100 = 0.01. Right?

There are two numbers near 0.475 that are multiples of 0.01, namely 0.47 and 0.48. Right?

Each of these differs from 0.475 by 0.005: 0.475 - 0.47 = 0.005, and 0.48 - 0.475 = 0.005. Right?

So these are the same distance from 0.475, and either could be considered to be "the nearest multiple of 0.01 to 0.475", just as two towns that are each 5 kilometers from you could both be called "the nearest town" (or neither could).

Since you need one answer, you can either choose one randomly (arbitrarily), or follow an arbitrary rule that tells us which to choose (such as the rule you have evidently been taught, to use the one whose last digit is even).

Is this longer version clearer? If not, tell me where you are unsure what I mean, or where you disagree.
My first question from your explanation is below:
You said above that ''This means that you want to find the closest number to 0.475 that is a multiple of 1/100 = 0.01. and There are two numbers near 0.475 that are multiples of 0.01, namely 0.47 and 0.48. Right?''
Here If I multiply (0.47 X 0.01) = 0.0047 and (0.48 X 0.01) = 0.0048, we get these two figures one is 0.0047 and another is 0.0048, So could you explain how these two figures are the closest number to 0.475 because, in the number 0.475, there are three digits after the decimal but here 0.0047 and 0.0048, there are four digits after the decimal? Please explain.
 
My first question from your explanation is below:
You said above that ''This means that you want to find the closest number to 0.475 that is a multiple of 1/100 = 0.01. and There are two numbers near 0.475 that are multiples of 0.01, namely 0.47 and 0.48. Right?''
Here If I multiply (0.47 X 0.01) = 0.0047 and (0.48 X 0.01) = 0.0048, we get these two figures one is 0.0047 and another is 0.0048, So could you explain how these two figures are the closest number to 0.475 because, in the number 0.475, there are three digits after the decimal but here 0.0047 and 0.0048, there are four digits after the decimal? Please explain.

Okay, it appears that your problem is not knowing what "multiple of" means. We say that x is a multiple of y if there is some integer n such that x = ny. So a multiple of 0.01 is any number that is an integer times 0.01: 0.01, 0.02, 0.03, 0.04, ... . Any number with only two decimal places is a multiple of 0.01. In particular, 0.47 is a multiple of 0.01 because it is 47 * 0.01.

It does not mean that we are multiplying our number by 0.01, as you have done here.

And when we talk about "rounding to the nearest hundredth", we mean finding the nearest of these numbers -- the nearest number with no more than two decimal places.
 
Okay, it appears that your problem is not knowing what "multiple of" means. We say that x is a multiple of y if there is some integer n such that x = ny. So a multiple of 0.01 is any number that is an integer times 0.01: 0.01, 0.02, 0.03, 0.04, ... . Any number with only two decimal places is a multiple of 0.01. In particular, 0.47 is a multiple of 0.01 because it is 47 * 0.01.

It does not mean that we are multiplying our number by 0.01, as you have done here.

And when we talk about "rounding to the nearest hundredth", we mean finding the nearest of these numbers -- the nearest number with no more than two decimal places.
I understand the above point.
But you already said above ''So a multiple of 0.01 is any number that is an integer time 0.01: 0.01, 0.02, 0.03, 0.04,... Any number with only two decimal places is a multiple of 0.01.''
Then why should we take .47 and .48, not .49, .50, .51 etc up to the digits with two decimal places? could you explain, please?
 
I understand the above point.
But you already said above ''So a multiple of 0.01 is any number that is an integer time 0.01: 0.01, 0.02, 0.03, 0.04,... Any number with only two decimal places is a multiple of 0.01.''
Then why should we take .47 and .48, not .49, .50, .51 etc up to the digits with two decimal places? could you explain, please?

You might initially consider all those numbers, but since you are looking for the one(s) closest to 0.475, you focus on the largest one less than 0.475 (0.47), and smallest one greater than 0.475 (0.48). Those are the two nearest.

Ordinarily, you would use the one of those that is nearest; in this case they are equally distant, so you have to choose one arbitrarily.
 
You might initially consider all those numbers, but since you are looking for the one(s) closest to 0.475, you focus on the largest one less than 0.475 (0.47), and smallest one greater than 0.475 (0.48). Those are the two nearest.

Ordinarily, you would use the one of those that is nearest; in this case they are equally distant, so you have to choose one arbitrarily.
I don't understand what you mean by ''you focus on the largest one less than 0.475 (0.47), and smallest one greater than 0.475 (0.48).'' Could you simplify the point above, please?
 
I don't understand what you mean by ''you focus on the largest one less than 0.475 (0.47), and smallest one greater than 0.475 (0.48).'' Could you simplify the point above, please?


Draw the number line with 0.475 and a few numbers with 2 sig digits around it: ... 0.45 0.46 0.47 0.475 0.48 0.49 ...
Which numbers are the closest to 0.475? Well, the one to the left and the one to the right from it. Consider 0.47 - it's the largest one of ..., 0.45, 0.46, 0.47 which is still less than 0.475. 0.48 is the smallest, which is still greater than 0.475.
 
Draw the number line with 0.475 and a few numbers with 2 sig digits around it: ... 0.45 0.46 0.47 0.475 0.48 0.49 ...
Which numbers are the closest to 0.475? Well, the one to the left and the one to the right from it. Consider 0.47 - it's the largest one of ..., 0.45, 0.46, 0.47 which is still less than 0.475. 0.48 is the smallest, which is still greater than 0.475.
Why did you call 0.48 smallest?
If I do it below still it would be correct?
450 460 470 475 480 490 500. Now which one is closer to 475 from the left and right? the answer would be 470 from the left and 480 from the right. Now 470 is the largest one of 450, 460 but still, less than 475 and 480 is greater than 775.
 
That's not what lev888 said. He said that, of the numbers listed, "0.45 0.46 0.47 0.475 0.48 0.49", and that are larger than 0.75, so "0.48 0.49", -.48 is the smallest.
 
That's not what lev888 said. He said that, of the numbers listed, "0.45 0.46 0.47 0.475 0.48 0.49", and that are larger than 0.75, so "0.48 0.49", -.48 is the smallest.
'that are larger than 0.75, so "0.48 0.49", -.48 is the smallest.' Could you tell me where 0.75 comes from?
 
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