# Is This Statement Correct?

1. 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.

2. I am not sure! I am confused just reading that statement!!

3. 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!

4. 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.

6. Yep it is true. By rounding it means 2.000,000 = 2 , dot being the decimal point

7. #7
Last edited: Sep 15, 2010
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]
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 ​
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

[/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 721000
7, 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/15712049124338963/lib/15712049124338963/Bio%20Files/The%20Atlantic%20Pacific%20rule.pdf

8. 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.

9. This makes sense.

10. 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

11. 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.

12. But in my textbook it says '20 as in 'there are 20 cars in the parking lot'' has 2 significant figures.

13. Yes true!

14. #14
Last edited: Sep 17, 2010

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 )

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15. I'm pretty sure it's a typo (^(oo)^)