All zeros to the left of the first non-zero digit are insignificant, and all zeros to the right of the first non-zero digit are significant unless they are the result of rounding.
Is This Statement Correct?
- Thread starter BigBlueSky
- Start date
I believe so, yes.
Here is basically what it is saying:
"All zeros to the left of the first non-zero digit are insignificant."
Example: 000000000000000000000000002 = 2
"All zeros to the right of the first non-zero digit are significant unless they are the result of rounding."
Example: 2000000000000000000000 = 2,000,000,000,000,000,000,000
I'm not sure what it means by rounding, sorry!
Here is basically what it is saying:
"All zeros to the left of the first non-zero digit are insignificant."
Example: 000000000000000000000000002 = 2
"All zeros to the right of the first non-zero digit are significant unless they are the result of rounding."
Example: 2000000000000000000000 = 2,000,000,000,000,000,000,000
I'm not sure what it means by rounding, sorry!
All zeros to the left of the first non-zero digit are insignificant, and all zeros to the right of the first non-zero digit are significant unless they are the result of rounding.
I am not totaly sure about the "unless they are the result of rounding" part. The first part I know is true, zeros to the left of the first non zero digit are insignificant, and all zeros to the right of the first non zero digit are significant.
It's not just as simple as the way it was presented in the OP. It depends on the number of zeroes present and whether there is a decimal point. I would say that the decimal point determines whether the zeroes are counted as significant or not.
Here's the way I was taught to determine the number of significant figures ...
[FONT=Arial,Bold][FONT=Arial,Bold]
[/FONT]
- in this case there are 3 significant figures
- 721000
http://www.murrieta.k12.ca.us/15712...38963/Bio Files/The Atlantic Pacific rule.pdf
Here's the way I was taught to determine the number of significant figures ...
[FONT=Arial,Bold][FONT=Arial,Bold]
The Atlantic/Pacific Rule for Determining Significant Figures
[/FONT][/FONT]1) look for the presence, or not, of a decimal point
- this will tell you which side to start counting from
- Pacific: left
- Atlantic: right
2) if there is a decimal point you start counting from the left side of the number
- starting from the very left side of the number, look for the first non-zero number
- count the first non-zero number and every number (0-9) after that
- example: 0.00010
- because there is a decimal point, we start from the left side of the
equation
- this will tell you which side to start counting from
- Pacific: left
- Atlantic: right
2) if there is a decimal point you start counting from the left side of the number
- starting from the very left side of the number, look for the first non-zero number
- count the first non-zero number and every number (0-9) after that
- example: 0.00010
- because there is a decimal point, we start from the left side of the
equation
L0.00010, and look for the first non-zero number
0.000[FONT=Arial,Bold]1[/FONT]0
- count that number and every number after that regardless of what
the number is (0-9)
- in this case there are 2 significant figures
- 0.000[FONT=Arial,Bold]10
0.000[FONT=Arial,Bold]1[/FONT]0
- count that number and every number after that regardless of what
the number is (0-9)
- in this case there are 2 significant figures
- 0.000[FONT=Arial,Bold]10
[/FONT]
3) if there is
[FONT=Arial,Bold]not [/FONT]a decimal point you start counting from the right side of the number
- starting from the very right side of the number, look for the first non-zero
number
- count the first non-zero number and every number (0-9) after that
- example: 721000
- because there is a decimal point, we start from the right side of the
equation 7210007, and look for the first non-zero number
721000
- count that number and every number after that regardless of what
the number is (0-9)
- starting from the very right side of the number, look for the first non-zero
number
- count the first non-zero number and every number (0-9) after that
- example: 721000
- because there is a decimal point, we start from the right side of the
equation 7210007, and look for the first non-zero number
721000
- count that number and every number after that regardless of what
the number is (0-9)
- in this case there are 3 significant figures
- 721000
http://www.murrieta.k12.ca.us/15712...38963/Bio Files/The Atlantic Pacific rule.pdf
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I think that means if you have a number like
1234.0009
and it gets rounded to
1234.0010
the last zero isn't needed.
As for the whole statement, I think the first part is fine. It's the "right of the first non-zero" that's confusing.
How bout:
"All zeros to the left of the first non-zero digit are insignificant, and all zeros to the right of the decimal point are significant unless they are the result of rounding."
That would especially be true if you're dealing with precision measurements. The more zeros, right of the decimal, the more precise the measurement.
All zeros to the left of the first non-zero digit are insignificant, and all zeros to the right of the first non-zero digit are significant unless they are the result of rounding.
The bolded portion of the statement is false. Zeros to the right of the first non-zero digit AND either: (a) to the right of the decimal point; or (b) between significant digits, are significant.
So, for example (significant digits colored red):
- 0.0060 = 2 significant digits
- 600.0 = 4 significant digits
- 606 = 3 significant digits
- 600 = 1 significant digit
aklein - this confuses me, see the portion in red:
3) if there is
not a decimal point you start counting from the right side of the number
- starting from the very right side of the number, look for the first non-zero
number
- count the first non-zero number and every number (0-9) after that
- example: 721000
- because there is a decimal point, we start from the right side of the
equation 7210007, and look for the first non-zero number
721000
- count that number and every number after that regardless of what
the number is (0-9)
- in this case there are 3 significant figures
- 721000
But there is NOT a decimal point. Is there a typo in this example? Because if there isn't, the directions make no sense. I went to the link for this and it is the same.
3) if there is
not a decimal point you start counting from the right side of the number
- starting from the very right side of the number, look for the first non-zero
number
- count the first non-zero number and every number (0-9) after that
- example: 721000
- because there is a decimal point, we start from the right side of the
equation 7210007, and look for the first non-zero number
721000
- count that number and every number after that regardless of what
the number is (0-9)
- in this case there are 3 significant figures
- 721000
But there is NOT a decimal point. Is there a typo in this example? Because if there isn't, the directions make no sense. I went to the link for this and it is the same.
But in my textbook it says '20 as in 'there are 20 cars in the parking lot'' has 2 significant figures.
But in my textbook it says '20 as in 'there are 20 cars in the parking lot'' has 2 significant figures.
The problem with numbers that end in 0 with no decimal place is that the number of significant figures is ambiguous. In reality, 600 may have 1, 2 or 3 significant figures, but we can't say for certain just by looking at the number. All we can say, without further information, is that it has at least 1. That's why people use scientific notation in situations where the number of significant figures needs to be definitive. Then you could clearly express 600 with the correct number of significant figures as follows:
(sorry, had to do as a picture, superscripts kept disappearing
)Attachments
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