Scientific Notation
In science we often have to deal with very large or very small numbers. To simplify writing these numbers a system of scientific notation was devised. Eg. 204 560 000 g = 0.0000000000094 m = 3.2 x 103 L = 4.67 x 10­7 L = To convert to scientific notation: if the number is greater than one (>1): move the decimal _________ until you reach the first number, count the number of places moved and then place this number in the exponent of x10?. eg. moved 3 places then it is ___________.
if the number is less than one (<1): move the decimal _________ until you reach the first number, count the number of places moved and then place this number as a negative in the exponent of x10?. eg. moved 4 places right then it is _________.
Convert the following into scientific notation or the number. 1) 5678 = _______________ 2) 3.56 x 10­4 = ______________
3) 6.909 x 102 = _______________ 4) 4 = _____________
5) 0.000800 = _________________ 6) 7.5400 x 104 = ____________
Significant digits
All measurements in science must be made with some sort of measuring device (eg scale, meter stick...). Different measuring devices have different degrees of precision (a measure of the exactness of the measurement). eg. What is the length of this clown fish?
1
For any measurement one uncertain digit is allowed to be included.
eg. if the temperature is reported as 32.7 ºC
Precision is indicated by the number is _________________. The more sig. digs, the greater the precision. See rules for counting significant digits... Mathematical computations must NOT introduce extra precision. Identify the number of significant digits for each of the following
1) 3782 m ____________________
2) 2000 g ______________________
3) 0.004 L ____________________
4) 0.9740 km ____________________
5) 1.010 cm ____________________
6) 0.09097 ºC _________________
7) 1000 people
8) 42 980 cats ___________________
When completing mathematical calculations, precision must be considered. (see rules on "Measurement, uncertainty and working ... " sheet) Complete the following calculations, consider significant digits. Put your final answer in scientific notation. 1) 3.2 x 5.708
2) 10.9 / 12.3470
3) 40.9 ­ 12.678
4) 0.0098 + 83 2