Write 4.2 as a mixed number and as an improper fraction. Write your answers in simplest form.
mixed number: [ ]
improper fraction: [ ]
To represent the decimal \(4.2\) as a mixed number and as an improper fraction in simplest form, we begin by observing that the number is composed of an integer part and a decimal part: \(4.2 = 4 + 0.2\). The decimal part \(0.2\) can be written as a fraction by looking at the place value of the last digit, which is the tenths place. Thus, \(0.2 = \frac{2}{10}\).
To express the fraction \(\frac{2}{10}\) in its simplest form, we divide both the numerator and the denominator by their greatest common divisor, which is \(2\). Therefore, \(\frac{2}{10} = \frac{2 \div 2}{10 \div 2} = \frac{1}{5}\). Combining this with the integer part \(4\), we get the mixed number \(4\frac{1}{5}\).
To convert the mixed number \(4\frac{1}{5}\) into an improper fraction, we multiply the integer part by the denominator and add the numerator to the result: \(4 \times 5 + 1 = 20 + 1 = 21\). Placing this over the original denominator gives \(\frac{21}{5}\). This fraction is in its simplest form because \(21\) and \(5\) share no common factors other than \(1\).
In real-world applications like cooking, you might find a recipe that calls for \(4.2\) cups of flour. Knowing how to convert this decimal into a fraction helps you use your measuring cups accurately. Since standard measuring cups are often marked in fractions like \(1/5\), representing \(4.2\) as \(4\frac{1}{5}\) allows you to measure precisely \(4\) full cups and one-fifth of a cup, ensuring your baking turns out perfectly.