# And Now, A Little Math Hooray!!. Measurements and Calculations Chapter 5.

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And Now, A Little Math Hooray!!

Measurements and Calculations Chapter 5

Remember that the first step in science is making an observation, 2 kinds are –Qualitative Description based on qualities (It is red) –Quantitative Measurements 2 parts – Number and unit

Scientific Notation Numbers used may be very large or very small This way we can make these numbers as a product of a number between 1 and 10 and the appropriate power of 10 93,000,000 can be written as 9.3 x 10 7 –Move decimal until number is between 1 and 10 (one number is to its left) –Count the number of spaces you moved it –If you moved it to the left, the number is positive –If you moved it to the right, the number is negative Try these –238,000=2.38 x 10 5 –1,500,000=1.5 X 10 6 –0.000167=1.67 x 10 -4

Units International System of Units (SI) Based on metric system kilo- hecto- deka- BASE deci- centi- milli-

5.3 Measurements of Length, Volume, and Mass Length – distance between 2 points –Meter –1 inch = 2.54 centimeters –Use rulers Volume – space occupied by a substance –Liter or cubic centimeters or milliliters –Use graduated cylinders Mass – quantity of matter in an object –Kilogram or grams –Use a balance

5.4 Uncertainty in Measurement Estimate required when falls between 2 graduations This final digit is an uncertain number Usually record all certain numbers plus first uncertain number These are called the significant figures

5.5 Rules for Significant Figures Nonzero numbers always count as significant figures –1457 has 4 sig figs Three classes of zeros –Leading Zeros – come before nonzero numbers are not significant 0.0025 has 2 sig figs

–Captive Zeros – between nonzero numbers are always significant 1.008 has 4 sig figs 43,082 has 5 sig figs –Trailing Zeros – to the right of the number are significant only if there is a decimal point 100 has 1 but 100. has 3 470,000 has 2 sig figs but 4.00 has 3 Exact numbers – From counting or a definition so have unlimited sig figs. Does not limit number –110 riders, 8 apples, 1 inch = 2.54 cm

Rounding Off >5 up, 5 up, <5 down In calculations, do all first and then round Sig Figs in calculations are also important –Multiplication or division Sig figs same as lowest = limiting 3 sig figs x 2 sig figs = 2 sig figs –Addition and Subtraction Limiting has smallest number of decimals 12.11 + 18.0 + 1.013 = 31.1 (1 decimal place)

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