5.6 Introduction and Key Insights

We also need to keep track of the decimal point when we multiply decimals. Consider this example that uses some familiar fractions:

$$\frac{1}{2}\times \frac{1}{2} = \frac{1}{4}$$.

When we write it with decimal expressions, it becomes:

$$0.5 \times 0.5 = 0.25$$.

This multiplication equation looks simple enough. After all, we know $$5\times 5 = 25$$, and $$25$$ appears in our final answer. However, it may seem a bit strange that the decimal point remained in front of the $$25$$ for the final answer. We can explain this by treating our decimals as fractions with 10s in their denominators. Namely:

$$0.5 \times 0.5 = \frac{5}{10} \times \frac{5}{10} = \frac{25}{100} = 0.25$$

It can be easier to carry this decimal-multiplication process out by thinking in terms of "moving the decimal place".