To determine the smallest measurement of length among the given values, we need to compare each of the given lengths. Here are the lengths provided:
1. [tex]\( 9 \times 10^{-6} \)[/tex] meters
2. [tex]\( 7 \times 10^{-5} \)[/tex] meters
3. [tex]\( 7 \times 10^1 \)[/tex] meters
4. [tex]\( 9 \times 10^2 \)[/tex] meters
Let's convert these values to a more comparable form:
1. [tex]\( 9 \times 10^{-6} \)[/tex] meters: This is [tex]\( 0.000009 \)[/tex] meters.
2. [tex]\( 7 \times 10^{-5} \)[/tex] meters: This is [tex]\( 0.00007 \)[/tex] meters.
3. [tex]\( 7 \times 10^{1} \)[/tex] meters: This is [tex]\( 70 \)[/tex] meters.
4. [tex]\( 9 \times 10^{2} \)[/tex] meters: This is [tex]\( 900 \)[/tex] meters.
Now we compare these numerical values:
- [tex]\( 0.000009 \)[/tex] meters
- [tex]\( 0.00007 \)[/tex] meters
- [tex]\( 70 \)[/tex] meters
- [tex]\( 900 \)[/tex] meters
From these values, it is clear that:
- [tex]\( 0.000009 \)[/tex] meters (or [tex]\( 9 \times 10^{-6} \)[/tex] meters) is much smaller than [tex]\( 0.00007 \)[/tex] meters.
- [tex]\( 0.000009 \)[/tex] meters is also much smaller than [tex]\( 70 \)[/tex] meters.
- [tex]\( 0.000009 \)[/tex] meters is significantly smaller than [tex]\( 900 \)[/tex] meters.
Therefore, the smallest measurement of length among the provided values is [tex]\( 9 \times 10^{-6} \)[/tex] meters.
