5.3 Introduction and Key Insights

Decimal expressions often appear in situations that involve measurements and quantification – in various corners of "the real world" and in lots of "hard sciences". Fractions or rational numbers are more likely to occur in purely mathematical discussions. We need to know how to convert between these two notations to keep the lines of communication open between those who prefer "pure math" and those who follow applied math (with real-world applications).

What kind of notation is better? Fraction or decimal? As a pure mathematician, the answer is clearly fraction notation. Obviously! But it really depends on the context. Rational numbers, such as $10/3$, tell us a lot, and we can apply them to lots of situations.

For example, Let's take the expression $10/3$. It could mean someone is trying to divide 10 objects into three equal piles, or it could refer to an unknown quantity $x$ that makes the equation $3x-10 = 0$ true. However, it might be more convenient to use the decimal approximation $10/3 \approx 3.33$. This expression allows us to quickly understand and estimate its numerical value (a bit beyond 3).