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Comparing two estimates of a quotient

Comparing two estimates of a quotient

IP 1
6 marks

Ann and Ben estimate \(\dfrac{0.0496}{0.00251}\). Ann rounds each number to \(1\) significant figure; Ben rounds each number to \(2\) significant figures.

  1. Find Ann's estimate and Ben's estimate.[2]
  2. The exact value is \(19.76\), correct to \(4\) significant figures. By comparing how much each denominator was changed, explain why Ann's estimate is much further from the exact value.[2]
  3. Without using a calculator, explain whether the exact value is more than or less than \(20\).[2]

Solution:

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Answer:(a) Ann \(16\dfrac23\), Ben \(20\) (b) Ann increases the denominator by about \(20\%\) (Ben by about \(0.4\%\)), which lowers the quotient by about a sixth (c) less than \(20\): the numerator is below \(0.05\) and the denominator above \(0.0025\)

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