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Scientists take measurements to estimate quantities and ensure data reliability. Every measurement has an inherent error, influenced by both the measuring instrument and the conditions during the measurement. Key concepts include measurement errors like parallax and meniscus, accuracy indicating closeness to a standard, and precision relating to repeatability. Significant figures reflect the certainty of measurements, with rules governing which digits are counted as significant. Correctly applying these principles is crucial in calculations to maintain valid results across addition, subtraction, multiplication, and division.
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MEASUREMENTS Every measurement is an Estimate. Subject to the error of the instrument or the error of the person measuring. The condition during measurement is also a factor. Affect person or instrument. Ex: rain, wind, temperature, instrument
Measurement error Parallax – error caused by viewing an object at an angle.
Measurement error Meniscus – curved surface of a liquid in a container caused by the attraction of the liquid to the container
Accuracy - how close a measurement is to a specific standard Precision – ability to get the same measurement repeatedly. how close measurements are to each other. accurate & precise accurate precise
Significant figures, or digits, are the amount of digits that areaccurate in a calculation. This is determined by the number of digits in the numbers of a calculation. The rules for determining significant figures are below. All non-zero numbers are significant A number having all portions before and after the decimal point are significant. Zeroes at the end of a number that does have a decimal point are significant. The decimal point makes the zeroes significant. In a decimal number, the last zero or number measured is significant. Zeroes at the end of a number that does not have a decimal point are not significant. In a decimal number starting with zeroes, the zeroes are not significant.
ADDING AND SUBTRACTING SIGNIFICANT FIGURES Numbers that are added or subtracted should have the answer rounded to thedecimal place of the number having the fewest number of DECIMAL PLACES. MULTIPLICATION AND DIVISION OF SIGNIFICANT FIGURES Numbers that are multiplied or divided should have the answer rounded to the decimal place ofthe number having the fewest number of SIGNIFICANT FIGURES.