Skill: Estimate products using compatible numbers

To estimate a product, replace one or both factors with nearby numbers that are easy to multiply. These are called compatible numbers. Multiples of $(10)$, $(100)$, and $(1{,}000)$ are often useful.

Example: Estimate $(47 \times 198)$.

1. Choose nearby compatible numbers:

$$47 \approx 50 \qquad\text{and}\qquad 198 \approx 200$$

2. Multiply the compatible numbers:

$$50 \times 200 = 10{,}000$$

3. State the estimate:

$$47 \times 198 \approx 10{,}000$$

So, the product is about $\boxed{10{,}000}$. The estimate does not have to be exact; it should be close enough to show the product’s size.