SCIENTIFIC NOTATION, SIGNIFICANT DIGITS, & METRIC CONVERSIONS SNC2D SCIENTIFIC NOTATION, SIGNIFICANT DIGITS, & METRIC CONVERSIONS

SCIENTIFIC NOTATION Scientists often have to work with very large or very small numbers. It’s a system that uses a simpler form of these numbers. In scientific notation, all numbers are written in the form: a x 10n In this form, a can be greater than or equal to 1 but less than 10 and n can be any value.

SCIENTIFIC NOTATION For large numbers, move the decimal place to the left. The number of times you move the decimal point to the left will be equal to the exponent on the base 10. Example: 1500 (the exponent will be +3) 1.5 x 103 For small numbers, move the decimal place to the right. Note, the exponent on the base is negative. Example: 0.0505 (the exponent will be -2) 5.05 x 10-2

SCIENTIFIC NOTATION On a scientific calculator, enter using the following sequence: 5 . 0 5 EXP or EE +/- 2 Practice converting the numbers below from standard form into scientific notation 8,200,000 = ______________________ 50,880,000,000,000 = ______________ 0.00012 = ________________________ 0.00000000458 = __________________ 8.2 x 106 5.088 x 1013 1.2 x 10-4 4.58 x 10-9

QUESTION What is the length of the screw?

QUESTION NOW ... what is the length of the screw? A ruler marked in millimeters can generally make a much more precise measurement than a ruler marked in centimeters.

SIGNIFICANT DIGITS Every experiment involves some uncertainty in measurement. Significant digits are CERTAIN digits (considered accurate) plus one UNCERTAIN (estimated) digit used in the measurement. For example, the length of the screw: 5.N Vs 5.1N The precision of a measurement can be shown by the number of significant digits in the value.

SIGNIFICANT DIGITS RULES & EXAMPLES Any non-zero digit is significant. Ex. 227.4 has four significant digits. Zeros used to space a number to the right of a decimal point are not significant. Leading zeros are not significant (to the left of non-zero digits) Ex. 0.000147 has only three significant digits. Trailing zeros, to the right of any non-zero digits, are not significant (when there is no decimal). Ex. 74,000 has only two significant digits. All other zeros are significant. Ex. 60.59 has 4 significant digits.

CALCULATING WITH SIGNIFICANT DIGITS ROUNDING RULE: Rounding after the last significant digit < 5 ... Leave it > 5 ... Round up = 5 ... Round to the even number Example: round numbers to 4 significant figures 12.364 12.366 12.365 12.3649 12.36501  12.36  12.37  12.36  12.36  12.37

CALCULATING WITH SIGNIFICANT DIGITS RULE: In any calculation, the number of significant digits in the answer cannot be greater than the number of significant digits of any measured value. For example, suppose you do the following calculation: 5.73 x 2.1 = 12.033  In this situation, the second measurement has the fewest significant digits. Therefore, the answer must also have just two significant digits and should be reported as 12.

CERTAINTY RULE FOR MULTIPLICATION & DIVISION The answer has the same number of digits as the least significant figure (regardless of placement). Ex. 77.3 x 0.56 = Ex. 2.541 x 4.01 = Ex. 539.7 / 40. = 43.288 = 43 10.18941 = 10.2 13.4925 = 13

PRECISION RULE FOR ADDITION & SUBTRACTION The answer has the same number of decimal places as the least number in the question. Ex. 187.6 + 54.321 = 241.921 = 241.9

METRIC CONVERSIONS Metric system: The system of units used by most scientists. Also known as System International (SI) units. In the metric system, different units for the same quantity are related to one another by prefixes. Each prefix represents a multiple of 10.

METRIC CONVERSIONS All the conversions are multiples of 10. Converting from one unit to another, such as from meters to centimeters, simply involves shifting the decimal point to the left or right.  Example: 12.56 meters = 1,256 centimeters = 0.01256 kilometers.  Follow the diagram in the handout. 

METRIC CONVERSIONS Tips for solving unit conversion problems: Always be aware of the unit you start with and the unit you have been asked for. When converting  any type of measures: To convert from a larger to smaller metric unit you always multiply To convert from a smaller to larger unit you always divide  

METRIC CONVERSIONS This is the metric conversion stair chart. You basically take a place value chart turn it sideways and expand it so it looks like stairs. The Latin prefixes literally mean the number indicated. Meter, liter or gram can be used interchangeably.