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

lev888 said:
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.
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'0.48 is the smallest, which is still greater than 0.475.' Could you explain how is it possible?
 
Indranil said:
'0.48 is the smallest, which is still greater than 0.475.' Could you explain how is it possible?
Click to expand...

Did you make that number line?

Code: 
[FONT=courier new] +----+----+----+----+----+----+----+----+
0.45      0.46      0.47  ^   0.48      0.49
                        0.475[/FONT]

It should be clear that 0.48 is the smallest number in our list that is greater than 0.475, and that 0.47 is the greatest number in the list that is less than 0.475. Keep in mind that 0.47 is the same as 0.470, which is clearly less than 0.475.

If you still wonder, PLEASE tell us what you are thinking. Just asking us to explain the same thing over and over with no new information can be very frustrating.
 
Indranil said:
'0.48 is the smallest, which is still greater than 0.475.' Could you explain how is it possible?
Click to expand...
It is not the clearest sentence possible although it is clear in context. What is meant is:

"Of all possible numbers expressed with two decimal digits, the greatest one less than 0.475 is 0.47 and the least one greater than 0.475 is 0.48."

Obviously, 0.479 is less than 0.48 and is greater than 0.475, but 0.479 is expressed using three decimal digits, not two, so it is NOT included in the set of numbers being discussed.
 
Indranil said:
'0.48 is the smallest, which is still greater than 0.475.' Could you explain how is it possible?
Click to expand...

You have a collection of elephant figurines on a shelf ordered from smallest to tallest. You bought a new one. How do you find the right spot for it? You compare it to the tallest elephant. Is new one taller? No. Ok, how about the next one? Etc. When you find one that's smaller than the new elephant, the previous elephant in the collection was "the smallest, which is still greater" than the new one.
 
Dr.Peterson said:
Did you make that number line?

Code: 
[FONT=courier new] +----+----+----+----+----+----+----+----+
0.45      0.46      0.47  ^   0.48      0.49
                        0.475[/FONT]

It should be clear that 0.48 is the smallest number in our list that is greater than 0.475, and that 0.47 is the greatest number in the list that is less than 0.475. Keep in mind that 0.47 is the same as 0.470, which is clearly less than 0.475.

If you still wonder, PLEASE tell us what you are thinking. Just asking us to explain the same thing over and over with no new information can be very frustrating.
Click to expand...
Ok, Why did you call '0.47 is the greatest and 0.48 is the smallest number as you mentioned 0.47 = 0.470, 0.48 = 0.480 and we can see that speaking of the line, only 0.49 is the greatest and 0.45 is the smallest?
 
Dr.Peterson said:
Did you make that number line?

Code: 
[FONT=courier new] +----+----+----+----+----+----+----+----+
0.45      0.46      0.47  ^   0.48      0.49
                        0.475[/FONT]

It should be clear that 0.48 is the smallest number in our list that is greater than 0.475, and that 0.47 is the greatest number in the list that is less than 0.475. Keep in mind that 0.47 is the same as 0.470, which is clearly less than 0.475.

If you still wonder, PLEASE tell us what you are thinking. Just asking us to explain the same thing over and over with no new information can be very frustrating.
Click to expand...

Indranil said:
Ok, Why did you call '0.47 is the greatest and 0.48 is the smallest number as you mentioned 0.47 = 0.470, 0.48 = 0.480 and we can see that speaking of the line, only 0.49 is the greatest and 0.45 is the smallest?
Click to expand...

Read carefully. What I called "our list" is the list of numbers with two decimal places:0.01, 0.02, ..., 0.45, 0.46, 0.47, 0.48, 0.49, and so on -- the multiples of .01. But I didn't say that 0.47 is "the greatest" of all of these; I said it is "the greatest number in the list that is less than 0.475". It is, is it not? And the fact that 0.47 is equal to 0.470 does not change this; those are the same number, not two different numbers.
 
Dr.Peterson said:
Did you make that number line?

Code: 
[FONT=courier new] +----+----+----+----+----+----+----+----+
0.45      0.46      0.47  ^   0.48      0.49
                        0.475[/FONT]

It should be clear that 0.48 is the smallest number in our list that is greater than 0.475, and that 0.47 is the greatest number in the list that is less than 0.475. Keep in mind that 0.47 is the same as 0.470, which is clearly less than 0.475.

If you still wonder, PLEASE tell us what you are thinking. Just asking us to explain the same thing over and over with no new information can be very frustrating.
Click to expand...
'It should be clear that 0.48 is the smallest number in our list that is greater than 0.475'
Comparing to which number, you mentioned the above quote?
 
Indranil said:
'It should be clear that 0.48 is the smallest number in our list that is greater than 0.475'
Comparing to which number, you mentioned the above quote?
Click to expand...

We are looking at ALL numbers with 2 decimal places. There are infinitely many such numbers. We can't list or draw them all. So we draw the number line in the neighborhood of 0.475 - from 0.45 to 0.49. We can use -100.00 to +100.00, it will not change anything.
Now, which number is the smallest and still greater than 0.475? We start 'on the right', let's say 100.00. Is it greater than 0.475? Yes. Is it the smallest? Doesn't look like it is. How about 50.00? 20.00? 1.00? We keep going to the left on the number line until we find the smallest number with 2 dec. places which is still greater than 0.475.
And the number is ............... 0.48.
Why?
1. It's greater than 0.475.
2. It's the smallest - the next 2 dec. places number to the left of 0.48 is 0.47, and it's less than 0.475.

Follow similar steps to find the greatest 2 dec. places number which is less than 0.475 - only we start to the left of 0.475 (we need a number less than 0.475), go right.
 
lev888 said:
We are looking at ALL numbers with 2 decimal places. There are infinitely many such numbers. We can't list or draw them all. So we draw the number line in the neighborhood of 0.475 - from 0.45 to 0.49. We can use -100.00 to +100.00, it will not change anything.
Now, which number is the smallest and still greater than 0.475? We start 'on the right', let's say 100.00. Is it greater than 0.475? Yes. Is it the smallest? Doesn't look like it is. How about 50.00? 20.00? 1.00? We keep going to the left on the number line until we find the smallest number with 2 dec. places which is still greater than 0.475.
And the number is ............... 0.48.
Why?
1. It's greater than 0.475.
2. It's the smallest - the next 2 dec. places number to the left of 0.48 is 0.47, and it's less than 0.475.

Follow similar steps to find the greatest 2 dec. places number which is less than 0.475 - only we start to the left of 0.475 (we need a number less than 0.475), go right.
Click to expand...
Now I got it. Thank you all for your kind efforts.
 
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