Solve Decimal Division: 11.3 ÷ 3.8 Step-by-Step

To solve the problem $\frac{11.3}{3.8}$, follow these steps:

• Step 1: Convert 11.3 and 3.8 into fractions.
• Step 2: Conduct the division using these fractions.
• Step 3: Simplify and convert to a mixed number if appropriate.

Step 1: Convert 11.3 and 3.8 to fractions:
$11.3 = \frac{113}{10}$ since the decimal point signifies tenths place.
$3.8 = \frac{38}{10}$

Step 2: Use the rule for fraction division, which is to multiply by the reciprocal:
$\frac{113}{10} \div \frac{38}{10} = \frac{113}{10} \times \frac{10}{38} = \frac{113}{38}$.

Step 3: Simplify $\frac{113}{38}$ by performing the division:
113 divided by 38 gives a quotient of 2 and a remainder of 37.
Thus, $\frac{113}{38} = 2\frac{37}{38}$.

Therefore, the division of $\frac{11.3}{3.8}$ results in $2\frac{37}{38}$.

Therefore, the solution to $\frac{11.3}{3.8}$ is $\mathbf{2\frac{37}{38}}$, which matches the second choice provided.