Write 2.3 as a mixed number and as an improper fraction. Write your answers in simplest form.
mixed number: [ ]
improper fraction: [ ]
To express the decimal \(2.3\) as a mixed number and an improper fraction, we first analyze the structure of the decimal. The number \(2.3\) consists of an integer part \(2\) and a decimal part \(0.3\). The decimal part \(0.3\) represents three-tenths, which can be written as the fraction \(\frac{3}{10}\). This fraction is already in simplest form because \(3\) and \(10\) have no common factors other than \(1\).
A mixed number consists of an integer followed by a proper fraction. Based on our analysis, we can combine the integer part \(2\) and the fractional part \(\frac{3}{10}\) to represent \(2.3\) as the mixed number \(2\frac{3}{10}\). Since \(\frac{3}{10}\) is in its simplest form, the mixed number \(2\frac{3}{10}\) is also in simplest form.
To convert the mixed number \(2\frac{3}{10}\) into an improper fraction, we multiply the integer part by the denominator of the fraction and add the numerator. This calculation is \((2 \times 10) + 3 = 20 + 3 = 23\). We then place this sum over the original denominator to get \(\frac{23}{10}\). Since \(23\) and \(10\) share no common factors other than \(1\), the fraction \(\frac{23}{10}\) is in simplest form.
Imagine you are measuring wood for a craft project. If you have a piece that is \(2.3\) meters long, you could describe this length in different ways depending on your tools. A tape measure might show it as \(2 \frac{3}{10}\) meters, which is easy to read. However, if you are calculating the total length of several such pieces, using the improper fraction \(\frac{23}{10}\) makes the multiplication and addition much easier to handle, showing how these forms serve different purposes in practical measurements.