Compare Fractions and Decimals: Determining the Relationship Between 1/4 and 0.4

To compare $\frac{1}{4}$ and $0.4$, we first convert $\frac{1}{4}$ to a decimal:

Step 1: Convert $\frac{1}{4}$ to a decimal.

$\frac{1}{4}$ is the same as dividing 1 by 4. Performing this division, we get:

$\frac{1}{4} = 0.25$

Step 2: Compare the decimals.

Now, we compare $0.25$ with $0.4$:

$0.25 < 0.4$

Therefore, the appropriate sign to use is <.

The comparison between $\frac{1}{4}$ and $0.4$ is $\frac{1}{4} < 0.4$.

Therefore, the correct choice is: $<$.