Question

What type of number we will the product 3.14 and 3/4 be

Answer 1

To determine the type of number resulting from the product of \(3.14\) and \(\frac{3}{4}\), we can perform the multiplication:

\[
3.14 \times \frac{3}{4}
\]

First, we can convert \(3.14\) into a fraction to make the multiplication easier:

\[
3.14 = \frac{314}{100}
\]

Now, multiplying this by \(\frac{3}{4}\):

\[
\frac{314}{100} \times \frac{3}{4} = \frac{314 \times 3}{100 \times 4} = \frac{942}{400}
\]

To simplify \(\frac{942}{400}\):

- The greatest common divisor (GCD) of \(942\) and \(400\) is \(2\).

Dividing both the numerator and the denominator by \(2\):

\[
\frac{942 \div 2}{400 \div 2} = \frac{471}{200}
\]

Thus, the result can be expressed as a fraction, \(\frac{471}{200}\).

Now we analyze what type of number this is:

- The number \(3.14\) is a decimal, which is a rational number.
- The fraction \(\frac{3}{4}\) is also a rational number.
- The product of two rational numbers is always a rational number.

Therefore, the product \(3.14 \times \frac{3}{4}\) is a rational number.

More specifically, since we can express it as \(\frac{471}{200}\), which does not equal any whole number, it is neither an integer nor a whole number. Thus, the product is a rational number that is not an integer.