two questions about precision of measurement

[shannon4]

I would appreciate some help here:

1. Amy's temp. is 98.6 degrees F. What is the precision of this temperature reading?

2. If precision is + or - 1/2 the smallest unit of measure, what is the LEAST possible length for 6.5cm?

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stapel - post edited to remove chat-speak.

 

[stapel]

1) What is your book's definition of "precision"?

2) What does your book mean by "unit of measure"? Does this refer to the half-centimeter value in "six and a half centimeters", or "centimeters" itself?

When you reply, please include your thinking on these exercises.

Thank you.

Eliz.

 

[shannon4]

My book doesn't have a definition regarding precision. I do have an answer in the answer key of: + or - .5 and 6.55 However, in my thinking, if the precision accuracy is given in the tenth's position, how can the answer in the answer key be given in the hundreth position. I would have the answer be 6.1. As for the question regarding temperature, I don't see that enough information is give to have the problem solved.

 

[stapel]

My book doesn't have a definition regarding precision....in my thinking, if the precision accuracy is given in the tenth's position....

Think about looking at the thermometer. It is calibrated by degrees and the drug-store thermometer you've got under your bathroom sink, meant for measuring your body temperature, is subdivided into tenths. That is, the most accurate marking on your thermometer is one-tenth of a degree.

Take your temperature. The result will be given to the nearest tenth of a degree. But does that mean that your temperature was exactly 99.3°? Or that, to the nearest tenth of a degree, your temperature was 99.3°?

While you're having a little lie-down, think about the limitations of the equipment. Your temperature, to the nearest tenth of a degree, was 99.3°, but that only means that your actual temperature was somewhere between 99.25° (and rounded up) and 99.34° (and rounded down). Your temperature could have been ±0.05° in either direction from 99.3°.

The result you got was accurate within the limitations of the equipment; it was not an absolute measure.

For further information (since your book does not discuss the topic), try doing a search for "precision", "accuracy", "measurement", and/or "significant digits".

Eliz.