Express each of the following as fraction is simplest form :
0.345

Answer

To express the decimal number 0.345 as a fraction in its simplest form, we can follow these steps:

### Step 1: Write the decimal as a fraction
The decimal 0.345 can be expressed as:
\[ \frac{0.345}{1} \]

### Step 2: Eliminate the decimal
Since there are three digits after the decimal point, we can multiply both the numerator and the denominator by 1000 (10^3) to eliminate the decimal:
\[ \frac{0.345 \times 1000}{1 \times 1000} = \frac{345}{1000} \]

### Step 3: Simplify the fraction
Now we need to simplify the fraction \(\frac{345}{1000}\). To do this, we will find the greatest common divisor (GCD) of 345 and 1000.

### Step 4: Find the GCD
We can check the factors of both numbers:
- The prime factorization of 345 is \(3 \times 5 \times 23\).
- The prime factorization of 1000 is \(2^3 \times 5^3\).

The common factor is 5.

### Step 5: Divide both numerator and denominator by the GCD
Now we divide both the numerator and the denominator by 5:
\[ \frac{345 \div 5}{1000 \div 5} = \frac{69}{200} \]

### Final Answer
Thus, the simplest form of the fraction representing 0.345 is:
\[ \frac{69}{200} \]

---