Express each of the following as fraction is simplest form :
12.725

Answer

To express the decimal 12.725 as a fraction in its simplest form, follow these steps:

### Step 1: Write the decimal as a fraction
The decimal 12.725 can be expressed as:
\[ 12.725 = \frac{12725}{1000} \]
This is because there are three digits after the decimal point, which means we divide by \(1000\).

### Step 2: Simplify the fraction
Now, we need to simplify the fraction \(\frac{12725}{1000}\). To do this, we will find the greatest common divisor (GCD) of the numerator and denominator.

### Step 3: Find the GCD
To find the GCD, we can start by dividing both the numerator and the denominator by their common factors.

First, we can divide both by \(5\):
\[ 12725 \div 5 = 2545 \]
\[ 1000 \div 5 = 200 \]
So, we have:
\[ \frac{12725}{1000} = \frac{2545}{200} \]

Next, we can divide again by \(5\):
\[ 2545 \div 5 = 509 \]
\[ 200 \div 5 = 40 \]
Thus, we have:
\[ \frac{2545}{200} = \frac{509}{40} \]

### Step 4: Check if the fraction is in simplest form
Now, we check if \(\frac{509}{40}\) can be simplified further. The numerator \(509\) is a prime number and does not share any common factors with \(40\) (which factors into \(2^3 \times 5\)). Therefore, \(\frac{509}{40}\) is in its simplest form.

### Final Answer
Thus, the decimal \(12.725\) expressed as a fraction in simplest form is:
\[ \frac{509}{40} \]

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