Math 170: Topic 02
Number representations (exact, approximate, accuracy, limitations)
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Recognize and appropriately deal with various
numeric representations and their
limitations.
- Correctly associate integer values with nominal and ordinal data.
For example, use numeric values to represent the scale of responses to
an opinion questionnaire.
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- Correctly differentiate between the infinite precision of
actual integer values and the limits of machine representations
of integer values. Explain the degree of inability
of the TI-84 to correctly express
the product of 345,231,734 and 942,208,123.
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- Correctly demonstrate that integers are "closed" under the operations of addition,
subtraction, multiplication, and counting number exponentiation,
but not under division and
negative integer exponentiation. For example, create an expression
with at least 3 distinct integer values using at least two of the basic
operations of addition, subtraction, multiplication, division, and
integer exponentiation to produce a result that is not an integer.
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- Correctly convert rational values between fractional form
and decimal form. For example, convert 0.368136813681... to
the fractional form of p/q where both p and q are integers.
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- Correctly distinguish between truncated and repeating representations
of rational numbers. For example, why is 1/7 not equal to 0.14285714257142857?
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- Correctly round rational values to a given number of decimal places.
For example, round 34.283453 to 4 decimal places.
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- Correctly distinguish between computed values for irrational numbers and the true
value of such numbers. For example, the TI-84 calculator gives the square root of ten as
3.16227766. Is this correct? If so, show that it is correct, and if not, explain why it is not correct.
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- Correctly convert between decimal representations
of values and scientific representations of those values.
For example, convert 0.0003428 to scientific notation, or convert
5.8734x10–4
to standard decimal representation.
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©Roger M. Palay
Saline, MI 48176
August, 2013