AC9M10N01Year 10NumberPractised on site

AC9M10N01 — Year 10 Number

Official Curriculum Content Description:

recognise the effect of using approximations of real numbers in repeated calculations and compare the results when using exact representations

Worked Examples (1)

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Example 1Repeated Approximations & Numerical Accuracy

A savings account grows by a factor of 1.012 each year. An algorithm approximates this as 1.01 at every intermediate step. Starting with an initial value of

1000

, calculate the absolute difference between the exact final value after

7

steps (using

1.012

) and the approximate final value (using

1.01

). (Round answer to 2 decimal places; enter number only)

Common mistake: Calculating single-step error instead of compounded multi-step roundoff, or rounding only once at end

Correct Answer:

14.95

Worked Solution:

1. Exact calculation:

1000 \times (1.012)^{7} = 1087.0852

2. Approximated calculation:

1000 \times (1.01)^{7} = 1072.1354

3. Absolute difference (accumulated roundoff error):

|1072.1354 - 1087.0852| = 14.95

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