Sure, let's determine the number of significant figures in the given length.
The length is provided in scientific notation as:
[tex]\[ 1.20407 \times 10^{10} \, \text{m} \][/tex]
Here's how to count the significant figures step by step:
1. Scientific Notation Overview: Scientific notation expresses numbers as a product of a coefficient and a power of 10. It is commonly used to represent very large or very small numbers.
2. Identify the Coefficient: The coefficient in the given length is [tex]\( 1.20407 \)[/tex].
3. Count the Significant Figures in the Coefficient:
- Each digit in the coefficient, [tex]\( 1.20407 \)[/tex], counts as a significant figure.
- Significant figures include all non-zero digits, any zeros between significant digits, and any trailing zeros in the decimal part of the number.
4. Digits in the Coefficient: The coefficient [tex]\( 1.20407 \)[/tex] comprises the digits 1, 2, 0, 4, 0, and 7.
5. Counting the Significant Figures:
- 1 is significant.
- 2 is significant.
- 0 is significant (since it is between 2 and 4).
- 4 is significant.
- Another 0 is significant (since it lies between 0 and 7).
- 7 is significant.
Thus, every digit in [tex]\( 1.20407 \)[/tex] is significant.
Combining all these points, the coefficient in scientific notation [tex]\( 1.20407 \)[/tex] contains:
[tex]\[ 1, 2, 0, 4, 0, 7 \][/tex]
So, the total number of significant figures in the length [tex]\( 1.20407 \times 10^{10} \, \text{m} \)[/tex] is 7.
