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## Measurement

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**Measurement**A quantity that has both a number and a unit**Scientific Notation**• A way of writing either very large or very small numbers. • One number to the left of the decimal point multiplied by a power of 10.**Accuracy**• A measure of how close a measurement comes to the true value . • To evaluate accuracy your measurement must be compared to the true measurement**Precision**• A measure of how close a series of measurements are to each other. • To evaluate precision two or more measurements must be compared to each other.**Determining Error**• Accepted value – the correct value based on reliable references • Experimental value – the value measured in the lab**Error = experimental value**- accepted value % error = lerrorl x 100 accepted value**Significant Figures (sig figs)**• in measurements always depend on the instrument being used for the measurement. • include all digits that are known plus one digit that is estimated.**All measured numbers are significant figures.**• All non-zero numbers are measured. • Zeros that are acting as place holders are not measured.**Is the zero measured?**• Leading zeros are never measured. • Captured zeros are always measured. • Trailing zeros are only measured if there is a decimal in the number.**Measurements must always be reported to the correct number**of sig figs because calculated answers often depend on the number of sig figs in the values used in the calculations.**Significant figures in calculations**• In general a calculated answer cannot be more precise than the least precise measurement from which it was calculated.**Sig figs in addition and subtraction**• Round your answer to the same number of decimal places as the measurement with the least number of decimal places.**Sig figs in multiplication and division**• Round your answer to the same number of significant figures as the measurement with the least number of sig figs.**How many sig figs?**• 0.05730 meters • 0.00073 grams • 8.750 x10-2meters • 40.007 liters • 1.072 grams • 98,000 meters**Round to 3 sig figs**• 87.073 meters • 4.3621 x 108grams • 0.0152 meters • 9009 centimeters • 0.001775 millimeters • 314.721 grams**Calculate and round correctly**• 61.2m + 9.35m +8.6m = • (5.3 x 104) + (1.3 x 103) = • (9.12 x 10-1) – (4.7 x 10-2) = • 34.61cm -17.3cm = • 14.2g + 8.73g + 0.912g = • 349.0m – 12.52m – 8.24m=**Calculate and round correctly**• 7.55m x 0.34m = • 2.10cm x 0.70m = • 2.4526m/ 8.4 = • 22.4cm x 11.3cm x 5.2cm = • 8432m/ 12.5 = • 1.26 x 104/ 1.7 x 10-2 =**International System of Units (SI)**• kilogram(kg) measures mass • meter(m) measures length • kelvin(K) measures temperature • second(s) measures time • Mole(mol) measures amount**Volume**• Is a derived unit. • SI unit of volume is the amount of space occupied by a cube that is 1 m along each edge • The liter is a common unit of volume = a cube 10cm on each edge.**Temperature**• The SI unit is the kelvin. The Kelvin temperature scale is directly related to kinetic energy. So zero energy = 0K • K = oC + 273 • oC = K - 273**Conversion Factors**• A ratio of equal measurements. • 1 meter = 100 centimeters • 1 m , 100 cm 100 cm 1 m**Dimensional Analysis**• A way to analyze and solve problems using the units, or dimensions , of the measurement.**How many minutes are in exactly one week.**• 10080 minutes**An experiment requires that each student use an 8.5-cm**length of Mg ribbon. How many students can do the experiment with 570-cm of ribbon available? • 67 students**Convert**• 0.044 km to meters • 4.6 mg to grams • 0.107 g to centigrams • 15 cm3 to liters • 7.38 g to kg • 6.72 s to milliseconds**The radius of the potassium atom is 0.227 nm. Express this**radius in centimeters. • 2.27 x 10-8 cm**Density**• Is the ratio of an objects mass to its volume. • It can also be thought of as an equality. • Density of gold=19.3g/cm3 • 19.3g Au = 1 cm3 Au**Gold has a density of 19.3 g/cm3. What is this density in**kilograms per cubic meter ? • 1930 kg/m3**A student finds a shiny piece of metal she thinks is**aluminum. She measures the mass to be 612 g and the volume to be 245 cm3. Is the sample aluminum? • Why or why not?**What is the volume of 4.62 g of mercury?**• What is the mass of 2.00 L of corn oil? • What is the volume of 1.25 kg of air?