Convert $3.2$ into a fraction.
We are given the decimal number \(3.2\) and tasked with converting it into a fraction in its simplest form. A terminating decimal can always be expressed as a fraction by considering its place value. The decimal part '2' occupies the tenths place, meaning \(0.2 = \frac{2}{10}\). Therefore, the number \(3.2\) can be written as \(3 + \frac{2}{10}\).
To express the decimal as a single fraction, we can write it as \(\frac{3.2}{1}\). To remove the decimal point, we multiply both the numerator and the denominator by \(10\):
\[\frac{3.2 \times 10}{1 \times 10} = \frac{32}{10}.\]
Now, we simplify the fraction \(\frac{32}{10}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD). The factors of 32 are 1, 2, 4, 8, 16, 32, and the factors of 10 are 1, 2, 5, 10. The greatest common divisor is 2. Dividing both by 2, we get:
\[\frac{32 \div 2}{10 \div 2} = \frac{16}{5}.\]
The fraction \(\frac{16}{5}\) is in its simplest form because 16 and 5 share no common factors other than 1. Thus, the decimal \(3.2\) expressed as a fraction is \(\boxed{\frac{16}{5}}\).
Understanding how to convert decimals to fractions is very useful in cooking and construction. For example, if a recipe calls for \(3.2\) cups of flour, it is often easier to measure this using a measuring cup if you know it equals \(3 \frac{1}{5}\) cups (since \(3.2 = \frac{16}{5} = 3 \frac{1}{5}\)). Similarly, in carpentry, dimensions are often given in fractions, so being able to convert between decimal and fractional measurements ensures precision when cutting materials.