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Uncertainty in Measurement. ACCURACY vs PRECISION ESTIMATING A DIGIT SIGNIFICANT FIGURES (SIG FIGS) ROUNDING TO APPROPRIATE SIG FIGS Created by P. Perkerson. ACCURACY.

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Uncertainty in measurement

Uncertainty in Measurement

ACCURACY vs PRECISION

ESTIMATING A DIGIT

SIGNIFICANT FIGURES (SIG FIGS)

ROUNDING TO APPROPRIATE SIG FIGS

Created by P. Perkerson


Accuracy
ACCURACY

  • Accuracy describes the nearness of a measurement to the standard or true value, i.e., a highly accurate measuring device will provide measurements very close to the standard, true or known values.

  • Example: in target shooting a high score indicates the nearness to the bull's eye and is a measure of the shooter's accuracy.


Precision
PRECISION

  • Precision is the degree to which several measurements provide answers very close to each other. It is an indicator of the scatter in the data. The lesser the scatter, higher the precision.

  • "repeatable, reliable, getting the same measurement each time."


Accuracy precision
ACCURACY & PRECISION

  • When making measurements, we want to be both accurate and precise!

  • Use the appropriate instrument & read it carefully.

  • We want the arrows close together and in or near the bull’s eye!


Measuring estimating
MEASURING & ESTIMATING

  • A measurement will always have some degree of uncertainty!

  • Use an estimated digit - “certain (known) numbers” plus one “ the uncertain number”.

  • How? First identify the scale (increments) of the instrument you are using. Then estimate the measurement one place value beyond the instrument’s scale.


So what is significant
So, what is significant?

  • Use sig figs to indicate degree of uncertainty

  • All non-zero digits (1,2,3…) are significant.

  • All captured zeroes (302) are significant.

  • Trailing zeroes are significant IF there is a decimal (.3400)

  • Leading zeroes are never significant (0.00456)


Exact numbers
Exact numbers:

  • Things that are counted. ( 10 marbles, 47 cars)

  • Definitions – 5280 feet in 1 mile

  • Conversion factors from a table or chart

    Have an indefinite number of significant figures. Therefore, they are not considered for rounding when used in calculations.


Identify the number of sig figs in each number below
Identify the number of sig figs in each number below.

  • A) 2305

  • B) 0.0263

  • C) 2.600

  • D) 2.3 X 105


Calculating with sig figs
Calculating with sig figs

  • When multiplying or dividing, round answer to the fewest number of sig figs given in the problem.

  • When adding or subtracting, round to the least precise place value given in the problem.

  • Do NOT consider exact values, conversion factors, values from a chart or table when deciding how many sig figs in answer!


Rounding to appropriate sig figs
Rounding to appropriate sig figs

  • Look one place value beyond needed sig fig. If digit is less than 5 number stays the same. If it is 5 or greater round up.

  • Example: round 7,634 to 2 sig figs. 2nd highest place value is hundreds place – look to the tens place. Digit is less than 5 so the 6 stays and the 3 & 4 are replaced with zeroes. 7,600