Write 5.87 as a mixed number and as an improper fraction. Do not try to simplify your answers.
mixed number:
improper fraction:
The decimal \(5.87\) consists of an integer part and a fractional part. We can separate it as:
\[5.87 = 5 + 0.87\]
The integer part is \(5\). The fractional part is \(0.87\), which represents eighty-seven hundredths. We can express this as a fraction by placing the digits after the decimal point over \(100\):
\[0.87 = \frac{87}{100}\]
Combining these, we get the mixed number:
\[5 \frac{87}{100}\]
To convert the mixed number \(5 \frac{87}{100}\) to an improper fraction, we multiply the integer part by the denominator and add the numerator:
\[5 \frac{87}{100} = \frac{5 \times 100 + 87}{100}\]
Performing the multiplication:
\[5 \times 100 = 500\]
Then, adding the numerator:
\[500 + 87 = 587\]
The resulting improper fraction is:
\[\frac{587}{100}\]
The decimal \(5.87\) is written as a mixed number and as an improper fraction as follows:
Mixed number: \(\boxed{5 \frac{87}{100}}\)
Improper fraction: \(\boxed{\frac{587}{100}}\)
In a measurement context, imagine you have a length of exactly \(5.87\) meters. If you need to report this in terms of whole meters and a fraction of a meter (for simple tool calibration) or as a single fraction of a meter (for manufacturing precision), you use these conversions. Representing the length as a mixed number, \(5 \frac{87}{100}\) m, helps identify the whole meter segments, while the improper fraction, \(\frac{587}{100}\) m, makes it easier to work with uniform units in calculation formulas.