Question

Question 14
The table shows the diameters of two objects.



Object Diameter (m)
Cloud-Water Droplet 10−5

Pinhead 0.001



How many times as great is the diameter of a pinhead as the diameter of a cloud-water droplet?



__ times as great

Answer 1

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.