Approximation Math Example 3

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Example 3

easy
Estimate 198×52198 \times 52 using rounding, then compute the exact answer and find the percent error.

Solution

  1. 1
    Round to 200×50=10,000200 \times 50 = 10{,}000.
  2. 2
    Exact: 198×52=10,296198 \times 52 = 10{,}296.
  3. 3
    Percent error: ∣10,000−10,296∣10,296×100=29610,296≈2.9%\dfrac{|10{,}000 - 10{,}296|}{10{,}296} \times 100 = \dfrac{296}{10{,}296} \approx 2.9\%.

Answer

Estimate 10,00010{,}000; exact 10,29610{,}296; percent error ≈2.9%\approx 2.9\%.
Rounding both factors to convenient numbers before multiplying gives a fast mental estimate. The resulting error is typically small when both roundings are modest, and the percent error quantifies how reliable the approximation is.

About Approximation

A value intentionally chosen to be close to but not exactly equal to the true value, with a known or estimated error.

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More Approximation Examples

Example 1 easy

Estimate [formula] to one decimal place without a calculator.

Example 2 medium

Use the approximation [formula] to estimate the circumference and area of a circle with radius [form

Example 4 medium

Use the first-order linear approximation [formula] to estimate [formula].

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