Is `5.25` a rational number ? Can you write it in the form p/q , where p and q are integers and `q ne 0` ?

Answer

To determine if `5.25` is a rational number and can be expressed in the form of `p/q` where `p` and `q` are integers and `q ≠ 0`, we can follow these steps:

### Step 1: Understand the definition of a rational number
A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

### Step 2: Convert `5.25` to a fraction
To express `5.25` in the form of a fraction, we can rewrite it as:
\[ 5.25 = \frac{525}{100} \]
This is because `5.25` can be seen as `5.25 = 5 + 0.25`, and `0.25` is equivalent to `\frac{25}{100}`.

### Step 3: Simplify the fraction
Now we simplify the fraction:
\[ \frac{525}{100} \]
To simplify, we can find the greatest common divisor (GCD) of `525` and `100`. The GCD is `25`.

Now, divide both the numerator and the denominator by `25`:
\[ \frac{525 \div 25}{100 \div 25} = \frac{21}{4} \]

### Step 4: Check if the denominator is not zero
In our simplified fraction `\frac{21}{4}`, the denominator is `4`, which is not equal to zero.

### Conclusion
Since we have expressed `5.25` as `\frac{21}{4}`, where both `21` and `4` are integers and `4 ≠ 0`, we conclude that `5.25` is indeed a rational number.

### Final Answer
Yes, `5.25` is a rational number and can be expressed in the form of `p/q` as `\frac{21}{4}`.

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