`a:b=4*77`, Ratio of `a:b=?`

Answer

To solve the problem where the ratio \( a:b = 4.77 \), we will convert this decimal into a fraction and express it in the simplest form.

### Step-by-Step Solution:

1. **Understand the Ratio**:
The ratio \( a:b = 4.77 \) means that for every 4.77 parts of \( a \), there are 1 part of \( b \).

2. **Convert Decimal to Fraction**:
To convert \( 4.77 \) into a fraction, we can express it as:
\[ 4.77 = \frac{477}{100} \]
This is because \( 4.77 \) can be read as \( 4.77 = \frac{477}{100} \) (moving the decimal point two places to the right).

3. **Express the Ratio**:
Now we can express the ratio \( a:b \) as:
\[ a:b = \frac{477}{100} \]
This means \( a = 477 \) and \( b = 100 \).

4. **Simplify the Ratio**:
The ratio \( a:b \) can be simplified if both numbers have a common factor. In this case, \( 477 \) and \( 100 \) do not have any common factors other than 1, so the ratio is already in its simplest form.

5. **Final Answer**:
Therefore, the ratio \( a:b \) is:
\[ a:b = 477:100 \]