In scientific notation, how are significant figures determined?

In scientific notation, significant figures are determined by counting all the digits that convey meaningful information about the precision of the measurement. This includes all non-zero digits, any zeros that are sandwiched between significant digits, and any trailing zeros in the decimal part of the number.

For example, in the scientific notation representation of a number, such as ( 1.23 \times 10^4 ), all three digits (1, 2, and 3) are significant. If a number were expressed as ( 0.00450 \times 10^3 ), the '4' and '5' are significant due to the non-zero digits and the trailing zero after the '5' contributes to the measurement's precision, totaling three significant figures.

This understanding emphasizes the importance of recognizing that significant figures reflect the accuracy of a measurement and are not influenced by positional zeros that do not affect the value's precision. Thus, the accurate determination of significant figures in scientific notation includes counting all digits that contribute meaningful information, leading to the answer that all digits are counted.