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Estimate products using compatible numbers

A whole-number product can be estimated by replacing one or both factors with nearby compatible numbers—often multiples of 10, 100, or 1,000, or numbers that combine easily—then multiplying the revised factors. The estimate should be close to, but need not equal, the exact product; its magnitude can be used to judge whether an exact calculation is reasonable, especially when both factors are changed. This scope excludes decimal or fraction products and formal error bounds.

Detailed Explanation: 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)(10), (100)(100), and (1,000)(1{,}000) are often useful.

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

  1. Choose nearby compatible numbers:
47≈50and198≈200 47 \approx 50 \qquad\text{and}\qquad 198 \approx 200
  1. Multiply the compatible numbers:
50×200=10,000 50 \times 200 = 10{,}000
  1. State the estimate:
47×198≈10,000 47 \times 198 \approx 10{,}000

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

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