A test tube contains $0.42$ cm$^3$ of liquid. A scientist wants to divide the liquid into samples of volume $7$ mm$^3$. The problem asks to find how many samples can the liquid be divided into.

1. Problem Description

A test tube contains $0.42$ cm$^3$ of liquid. A scientist wants to divide the liquid into samples of volume $7$ mm$^3$. The problem asks to find how many samples can the liquid be divided into.

2. Solution Steps

First, we need to convert the volume of the liquid in the test tube from cm$^3$ to mm$^3$.

Since $1$ cm $= 10$ mm, we have $1$ cm$^3 = (10 \text{ mm})^3 = 1000$ mm$^3$.

Therefore, $0.42$ cm$^3 = 0.42 \times 1000$ mm$^3 = 420$ mm$^3$.

Now, we have the volume of the liquid in the test tube as $420$ mm$^3$, and the volume of each sample is $7$ mm$^3$.

To find the number of samples, we need to divide the total volume by the volume of each sample.

Number of samples = $\frac{\text{Total volume}}{\text{Volume of each sample}} = \frac{420 \text{ mm}^3}{7 \text{ mm}^3} = 60$.

3. Final Answer

$60$