CH 2: Scientific Measurement Renee Y. Becker CHM 1025 Valencia Community College
Measurements • Measurement • A number with an attached unit Examples: 15 inches 3 cups 36 cm Every measurement must include units!!
Example 1: Measurements In the following, what are the measurements and what are the units? a) 12 trees b) 2.3 mm c) 100 ¢
Measurements • Instrument • A device for recording a measurement • Examples: Ruler (length), electronic balance (mass), Graduated cylinder (volume)
Uncertainty • An instrument may give a very sensitive reading, but EVERY measurement has UNCERTAINTY • No measurement instrument is perfect and neither is the person using it
Example 2: Length Measurements • If we need to measure the length of this candycane, which ruler should we use? Why?
Mass • Mass • Measure of the amount of matter it possesses • Measured by a balance • Not affected by gravity • Typical units: kilogram (kg), gram (g), pound (lb), ounce (oz) • Weight • Force exerted by gravity on an object
Example 3: Mass • Would you have the same mass on the moon as on Earth? Why? • Would you have the same weight on the moon as on Earth? Why?
Volume • Volume • The amount of space occupied by a solid, gas, or liquid • Graduated cylinder, pipet, buret, volumetric flask, syringe • Typical units: milliliter (mL), Liter (L), centimeter cubed (cm3), quart (qt), gallon (gal),
Accuracy, Precision, and Significant Figures in Measurement • Accuracy is how close to the true value a given measurement is. • Precision is how well a number of independent measurements agree with one another.
Accuracy, Precision, and Significant Figures in Measurement • Significant Figures are the total number of digits in the measurement. • The results of calculations are only as reliable as the least precise measurement!! • Rules exist to govern the use of significant figures after the measurements have been made.
Accuracy, Precision, and Significant Figures in Measurement • Rules for Significant Figures: • Zeros in the middle of a number are significant • Zeros at the beginning of a number are not significant • Zeros at the end of a number and following a period are significant • Zeros at the end of a number and before a period may or may not be significant.
Example 4: Significant Figures How many Sig. Figs ? a) 0.000459 b) 12.36 c) 36,450 d) 8.005 e) 28.050
Accuracy, Precision, and Significant Figures in Measurement • Rules for Calculating Numbers: • During multiplication or division, the answer can’t have more sig figs than any of the original numbers.
Example 5: Significant Figures • 238.5 x 79 = • 12 / 0.1272 = • 0.2895 x 0.29 = • 32.567 / 22.98 =
Accuracy, Precision, and Significant Figures in Measurement -During addition or subtraction, the answer can’t have more digits to the right of the decimal point than any of the original numbers.
Example 6: Significant Figures • 238.5 + 79 = • 12.3 - 0.1272 = • 0.2895 + 0.29 = • 32.567 - 22.98 =
Accuracy, Precision, and Significant Figures in Measurement • Rules for Rounding Numbers: • If the first digit removed is less than 5 - round down • If the first digit removed is greater than 5 - round up • If the first digit removed is 5 and following numbers are nonzero - round up • If the first digit removed is 5 and following numbers are zero - round down • Only final answers are rounded off, do not round intermediate calculations
Example 7: Rounding Round off each of the following measurements • 3.774499 L to four significant figures (b) 255.0974 K to three significant figures (c) 55.265 kg to four significant figures
Example 8: Accuracy & Precision Which of the following is precise but not accurate?
Scientific Notation • Changing numbers into scientific notation • Large # to small # • Moving decimal place to left, positive exponent 123,987 = 1.23987 x 105 • Small # to large # • Moving decimal place to right, negative exponent 0.000239 = 2.39 x 10-4 • Correct scientific notation: #.#### x 10n
Scientific Notation • How to put into calculator??
Example 9: Scientific Notation Put into or take out of scientific notation • 87542 • 2.1956 x 10-3 • 0.784 • 2.78 x 106 • 92000
Significant Figures • When we count something, it is an exact number. • It has an infinte number of significant figures