CHEM 210 1st Edition Lecture 4Outline of Last LectureII. Units of MeasurementsA. SI Units of MeasurementIII. Converting Between MeasurementsIV. Temperature ScalesOutline of Current Lecture V. Significant FiguresA. Rules For Significant FiguresB. Addition and SubtractionC. Multiplication and DivisonD. Rules for RoundingVI. Precision and AccuracyVII. Systematic Error and Random ErrorCurrent LectureWhen solving numerical problems, it is important to use the correct number of significant figures. Your answer should include the same number of significant figures as the value with the least number of significant figures. There are rules however, to count which digits are and which ones are not significant figures. Any non-zero digit is always significant. If there are zeros after a decimal point, those are significant. Zeros to the left of non-zero digits are not significant. For example, 2.345 has 4 significant figures. 10.00 also has 4 significant figures because of the decimal point, however 1000 only has 1 significant figure. 0.0020 has only 2 significant figures even though it has a decimal point because zeros to the left of non-zero digits are not significant. The more significant figures a number has, the more accurate it is. When adding and subtracting numbers, the answer has the same number of decimal places as there are in the measurement with the fewest decimal places. Ex; 83.5 mL + 23.28 mL = 106.78 mL which would then round off to 106.8 mL.These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.When multiplying and dividing numbers, the answer has the same number of significant figures as in the measurement.Ex; 9.2 cm X 6.8 cm X 0.03744 cm = 23.4225 cm cubed which then round down to 23 cm cubed because 9.2 only has 2 significant figures. When deciding whether to round up or down, it is important to look at the integer on the right of the number you are rounding. If it is greater than 5, you round up. If it is less than 5, you round down. If the number equals 5, you round up if it is odd and it is left unchanged if itis even. Ex; 2.34 rounds down to 2.3, 6.89 rounds up to 6.9, 17.75 rounds up to 17.8 because 7 is an odd number, 17.65 stays at 17.6 because 6 is an even number.Precision and AccuracyPrecision refers to reproducibility or how close the measurements are to each other. Accuracy refers to how close a measurement is to the real value. For example, if a student is throwing darts at a target and they hit it right in the bull’s-eye every time, they are very accurate. However, if the student is throwing darts and they miss the bull’s-eye every time but they their darts land in one area on the target, they are very precise. Systematic Error and Random ErrorSystematic error occurs when values are all higher or all lower than the actual value, while random error occurs when some values are lower and some value are higher than the actual value. For example, if a student should have obtained the value of 10.8 but all of their values turned out to be 5.4, 2.0, 2.25, 6.3, and 4.44, that is systematic error because all of the values are lower than 10.8. However, if the student recorded values such as 12.3, 1.23, 5.34, 14.3 and 4.4, then that would be random error because the values are all over the place and some are higher than the actual value, while some are lower than the actual