The problem asks us to compare $49\%$ with the fraction $\frac{45}{64}$ and determine which sign ($>$, $<$, or $=$) makes the statement true.

1. Problem Description

The problem asks us to compare $49\%$ with the fraction $\frac{45}{64}$ and determine which sign ($>$, $<$, or $=$) makes the statement true.

2. Solution Steps

First, we need to convert either the percentage to a fraction or the fraction to a percentage. It's easier to convert the fraction to a percentage. To do this, we divide 45 by 64 to obtain a decimal and then multiply by 100 to convert the decimal to a percentage.

$\frac{45}{64} \approx 0.703125$

Now, we convert this decimal to a percentage by multiplying by 100:

$0.703125 \times 100 = 70.3125\%$

So, $\frac{45}{64} \approx 70.3125\%$. Now we compare $49\%$ with $70.3125\%$. Since $49$ is less than $70.3125$, we have:

$49\% < 70.3125\%$

Therefore, $49\% < \frac{45}{64}$.

3. Final Answer

$<$