To find out how many times greater the diameter of a pinhead is compared to the diameter of a cloud-water droplet, you can divide the diameter of the pinhead by the diameter of the cloud-water droplet.
The diameters are as follows:
- Cloud-Water Droplet: \( 10^{-5} \) m
- Pinhead: \( 0.001 \) m, which can also be expressed as \( 10^{-3} \) m.
Now, we can calculate the ratio:
\[ \text{Ratio} = \frac{\text{Diameter of Pinhead}}{\text{Diameter of Cloud-Water Droplet}} = \frac{10^{-3}}{10^{-5}} \]
When dividing powers of ten, you subtract the exponents:
\[ \frac{10^{-3}}{10^{-5}} = 10^{-3 - (-5)} = 10^{-3 + 5} = 10^{2} \]
This means:
\[ 10^{2} = 100 \]
Thus, the diameter of a pinhead is 100 times as great as the diameter of a cloud-water droplet.
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