1. Approximation, Bounds, Percent Error, and Estimation
Number and Algebra
Topic 1.1, 1.6

2. Why do we use units of measure? Why not just state a value?
When stating answers or expressing the results of a mathematical process, IB requires you to supply units of measure (or use the appropriate symbols) to denote distance, angle measure, area, volume, currency, temperature, or time.
Who has designed our current, common units of measure?

3. Why do we use standard form (i.e.: scientific notation)?
Imperial Units and Metric System
imperial established in 1824 in England
metric common measures compared to the base unit
kilo times k
centi one hundredth c
milli one thousandth m
2.5 km = m = cm = mm
kg = g = 398 cg = mg
Which of the values’ representations might be considered the “best” form?
Why do we use standard form (i.e.: scientific notation)?

4. Scientific Notation writing a number in the form where and
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writing a number in the form where and
do not write down the number using “E” (calculator speak)

5. Significant Figures
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IB usually allows or expects you to round to three significant figures (“3 s.f.”), but may request more or less significant figures in a question
can use scientific notation as an intermediate step
zeros that precede and follow the first and last non-zero digits are not significant figures

6. Accuracy based on measurement device and procedure
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based on measurement device and procedure
accurate to the smallest division in the scale
measure: range of possible lengths:

7. Accuracy based on measurement device and procedure
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based on measurement device and procedure
accurate to the smallest division in the scale
measure: range of possible lengths:

8. Accuracy based on measurement device and procedure
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based on measurement device and procedure
accurate to the smallest division in the scale
measure: range of possible lengths:

9. Example
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One side length of an regular quadrilateral is measured to the nearest whole unit as 11 cm. What are the boundary values for:
one side length?
perimeter?
area?

11. number of seats in Paxon Auditorium What’s your estimate? _________
Approximation
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value close to, but not equal to, its true value
estimation: approximation found by judgment instead of a more accurate determination
number of seats in Paxon Auditorium
What’s your estimate? _________
rows: 17 seats in middle row: 48
Barnett’s estimated number of seats:

12. What was your error? _________ = _____
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error = approximate value – exact value
actual seats: 843
Mrs. Barnett’s error: 816 – 843 = -27
“Therefore, Barnett’s estimate was 27 seats less than the actual number of seats.”
What was your error? _________ = _____

13. Percentage Error compares error with the exact value : exact value
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compares error with the exact value
: exact value
: approximate value
Barnett’s percentage error