Question

Significant figures depend on _________ number of significant figures in the given data.

Answer 1

Significant figures:

The number of digits used to express a measured or calculated quantity is known as the significant figures. We can show a number's correctness by demonstrating significant figures. The following are the digits that are significant:

1. Non-zero digits are significant. For example: $18657$ has five significant figures
2. Any zeros between two non-zero digits are significant. Foe example: $106.0047$ has seven significant figures.
3. A final zero or trailing zeros in the decimal positions are significant. For example: $20.00$ has four significant figures.

The following are the rules of significant numbers:

1. When doing addition or subtraction, the solution should have the same number of decimal places as the term with the fewest decimal places. For example: $436.22+0.2256=436.4456$. Here the the former has two digits after decimal and the latter has one digit after decimal. Therefore the result should have as many number of digits as the term with least number of digits after decimal i.e. one digit and hence the answer should be $436.4$
2. The result should have the same amount of significant figures as the term in the multiplication and division that has the fewest significant figures. For example:
   1. $0.00435\times 4.6=0.02001$. Here the former has three significant figures and the latter has two significant figures and so the answer should have significant figures as many as the term with number of significant figures i.e. two and hence the answer should be $0.020$ which has two significant figures.
   2. $0.00032÷11.2=0.00002857$. Here the former has two significant figures and the latter has three significant figures and so the answer should have as many significant figures as that of the term with least number of significant figures i.e. two and hence the answer should be rounded off to $0.000029$which has two significant figures.
3. For exact numbers, like integers, the number of significant figures is thought to be infinite i.e. $2$ is understood to be $2.0000000.....$ with an infinite number of significant figures.

Hence the significant figures depend on the least number of significant figures in the given data.