I'm a little confused when it comes to significant figures. Where it doesn't make sense to me is when zeros come before and after a number.
For example:
My book states that zeros that come before a digit are NEVER significant. Now this makes sense if you have a number like 0.123 which would have three significant figures... But the book gives the example of 0.0055 which it says only has two significant figures. This isn't logical to me! 0.0055 IS NOT the same as .55 so how can those two zeros after the decimal point, not be significant?
The other part that confuses me is when zeros come after the numbers. For example, .3400 has four significant figures. This isn't logical to me either. Isn't .3400 the same as .34? I feel like these rules are wrong and should be switched around.
Is there something I'm not understanding about significant figures that would shed some light on these rules?
I can understand why you might find the rules for significant figures confusing, but once you understand their purpose, it might make more sense.
Significant figures are a way to represent the precision of a measurement or calculation. They help to communicate the degree of certainty or uncertainty in a value. The rules for determining the significant figures are as follows:
1. Non-zero digits are always significant. So, in your example of 0.123, all of the digits (1, 2, and 3) are significant because they are non-zero.
2. Zeros between non-zero digits are always significant. For example, in 506, all three digits are significant.
Now, let's address your specific questions:
1. Zeros that come before a digit in a number smaller than 1 are not significant. This is because they are just placeholders and do not represent actual measurements. So, in the example of 0.0055, the significant figures are only the non-zero digits (5 and 5), giving you two significant figures. You're correct that 0.0055 is not the same as 0.55, but significant figures are not meant to convey the magnitude of a value, only the precision.
2. Zeros that come after the decimal point and after significant digits are significant. In your example of 0.3400, all four digits (3, 4, 0, and 0) are significant because they represent measurements or calculations with a certain precision. Adding trailing zeros after the significant figures indicates that the value has been measured or calculated to that level of precision.
I hope this explanation clarifies the concept of significant figures for you. Remember, significant figures are not about the size or worth of a number, but rather about its precision.