I'm having a hard time with significant figures. Any help would be appreciated.
The first one is 0.0000000502. I put that it has three significant figures. Is this correct?
The other numbers I haven't a clue about are:
5.52
299,792,458
206,265
I get the jist of it, but I'm still struggling with the concept.
0.0000000502 = 3 sig. figures
5.52 = 3
299,792,458 = 9
206,265 = 6
Understanding significant figures can be challenging at first, but with practice, it becomes easier. Significant figures are used to represent the precision or uncertainty of a measured or calculated quantity. Here's a breakdown of how to determine the number of significant figures in a given number:
1. Non-zero digits: All non-zero digits are always significant. In your first example, the number 0.0000000502 has three non-zero digits (5, 0, and 2), so it indeed has three significant figures.
2. Leading zeros: Leading zeros are the zeros that appear before any non-zero digits. They are not significant and do not count towards the total significant figures. For example, in the number 0.0000000502, the leading zeros (after the decimal point) are not significant.
3. Captive zeros: Captive zeros are zeros that are located between non-zero digits. They are always significant. In the number 5.52, both 5 and 2 are non-zero digits, and the zero in the middle is a captive zero, making this number have three significant figures.
4. Trailing zeros: Trailing zeros are zeros that appear at the end of a number without a decimal point. Their significance depends on whether they are significant or not. In general, trailing zeros are significant only if they are after the decimal point or if they are specifically indicated. For example, in the number 299,792,458, there are no trailing zeros since they do not add any extra precision to the value. So, this number has nine significant figures.
5. Exact numbers: Exact numbers are those that are known with certainty and do not limit the number of significant figures in a calculation. For example, the number 206,265 is considered exact since it does not involve any uncertainty or measurement. Therefore, it has six significant figures.
Remember to apply these rules when evaluating each digit's significance in a number to determine the total number of significant figures.
To summarize:
1. 0.0000000502 has three significant figures.
2. 5.52 has three significant figures.
3. 299,792,458 has nine significant figures.
4. 206,265 has six significant figures.
With practice, you will become more confident in determining significant figures accurately.