To determine the number of significant figures in the given measurement [tex]\( 3.57 \times 10^9 \)[/tex] nm, we need to follow these steps:
1. Identify the significant figures in the base number:
- The given length is expressed in scientific notation as [tex]\( 3.57 \times 10^9 \)[/tex].
- In scientific notation, the significant figures are found within the base number (the part before the exponent).
- Here, the base number is [tex]\( 3.57 \)[/tex].
2. Count the significant figures in the base number [tex]\( 3.57 \)[/tex]:
- All non-zero digits are significant.
- So, for [tex]\( 3.57 \)[/tex]:
- The digits 3, 5, and 7 are all non-zero and therefore significant.
- As a result, the base number [tex]\( 3.57 \)[/tex] has 3 significant figures.
However, it's important to account for the notation details. When working with scientific notations:
- Exponents (like [tex]\( \times 10^9 \)[/tex]) do not affect the number of significant figures in the base number.
Given the steps outlined, the number of significant figures in the measurement [tex]\( 3.57 \times 10^9 \)[/tex] nm is:
[tex]\[
3
\][/tex]
