Question

Solomon needs to distribute ( \frac{3}{4} ) gallons of paint among 3 ( \frac{1}{2} ) gallon containers. How many gallons of paint will be in each container? Write the answer in scientific notation form.

Answer 1

To find out how many gallons of paint will be in each container, we need to divide the total amount of paint, \( \frac{3}{4} \) gallons, by the number of containers, which is 3 (or \( \frac{1}{2} \)) gallon containers.

First, we need to determine how many \( \frac{1}{2} \) gallon containers are being used:

\[
\text{Number of containers} = 3
\]

Now, we divide the total amount of paint by the number of containers:

\[
\text{Amount of paint per container} = \frac{3}{4} \div 3
\]

This division can be simplified by multiplying by the reciprocal:

\[
\frac{3}{4} \div 3 = \frac{3}{4} \times \frac{1}{3} = \frac{3 \times 1}{4 \times 3} = \frac{3}{12}
\]

Now we can simplify \( \frac{3}{12} \):

\[
\frac{3}{12} = \frac{1}{4}
\]

Thus, each \( \frac{1}{2} \) gallon container will be filled with \( \frac{1}{4} \) gallons of paint.

Next, we need to convert \( \frac{1}{4} \) into scientific notation.

\[
\frac{1}{4} = 0.25
\]

In scientific notation, \( 0.25 \) can be represented as:

\[
2.5 \times 10^{-1}
\]

So, the amount of paint in each container, expressed in scientific notation, is:

\[
\boxed{2.5 \times 10^{-1}} \text{ gallons}
\]