The problem is to calculate the division of two decimal numbers: $4.65 \div 3.5$.

1. Problem Description

The problem is to calculate the division of two decimal numbers: $4.65 \div 3.5$.

2. Solution Steps

To divide the decimal numbers, we first multiply both the dividend and the divisor by 10 until the divisor becomes an integer. In this case, we multiply both by 10 to get $46.5 \div 35$.

Now we perform long division.

$46.5 \div 35 = ?$

First, how many times does 35 go into 46? It goes in 1 time.

$1 \times 35 = 35$

$46 - 35 = 11$

Bring down the 5 to get

1

1

5.

Now, how many times does 35 go into 115? It goes in 3 times.

$3 \times 35 = 105$

$115 - 105 = 10$

We add a 0 to the dividend and bring it down to get

1

0

0.

How many times does 35 go into 100? It goes in 2 times.

$2 \times 35 = 70$

$100 - 70 = 30$

Add a 0 to the dividend and bring it down to get

3

0

0.

How many times does 35 go into 300? It goes in 8 times.

$8 \times 35 = 280$

$300 - 280 = 20$

Add a 0 to the dividend and bring it down to get

2

0

0.

How many times does 35 go into 200? It goes in 5 times.

$5 \times 35 = 175$

$200 - 175 = 25$

The division could continue but, given the context, it appears they are looking for 2 or 3 digits of accuracy.

So $4.65 \div 3.5 \approx 1.3285$

Since the hundredths place is the same as the first dividend, let's make one more division.

$4.65 \div 3.5 = 46.5 \div 35 = 1.3285... \approx 1.33$

3. Final Answer

1.33