Scientific Notation Significant Digits Physics Mr. Villa

In any measurement, the number of significant figures is critical. The number of significant figures in a result is simply the number of figures that are known with some degree of reliability.  The number 13.2 is said to have 3 significant figures. The number 13.20 is said to have 4 significant figures.

Significant Figures Rules for deciding the number of significant figures in a measured quantity: (1) All nonzero digits are significant: 1.234 g has 4 significant figures, 1.2 g has 2 significant figures. (2) Zeroes between nonzero digits are significant: 1002 kg has 4 significant figures, 3.07 mL has 3 significant figures.

Significant Figures (3) Leading zeros to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point: 0.001  has only 1 significant figure, 0.012 g has 2 significant figures. (4) Trailing zeroes that are also to the right of a decimal point in a number are significant: 0.0230 mL has 3 significant figures, 0.20 g has 2 significant figures.

Practice Significant Figures 1.  1.05  =     2.  0.0023 =   3.  4.566 = 4.   5.9  =         5.   3.00005 =   6.  845.6 = 7.   0.2 =       8.   5.55 =       9.   0.043 =

Scientific Notation A x10b Where, A is a real number b is an integer Scientific notation is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation. In scientific notation all numbers are written like this: Where, A is a real number b is an integer Example A x10b Ordinary decimal notation Scientific notation (normalized) 200 2×10^2 4,000 4×10^3 4,880,000,000 4.88×10^9 0.0000000091 9.1×10^−9

Scientific notation Examples 500 in scientific notation is written like this 5.0x102 The exponent 2 that is on top of the 10 is because you moved the decimal 2 spots. If the number does not have a decimal like 500 then always put an imaginary decimal at the end.

Scientific Notation Big Numbers (positive exponent): The exponent refers to the number of zeros that follow the 1. Moving the decimal to the left example: 2094 2.094x10^3 101 = 10 = 10x1 102 = 100 = 10 x 10 103 = 1,000 = 10x10x10 104 = 10,000 = 10x10x10x10 Small Numbers (negative exponent) Negative notations indicate numbers smaller than 1. Moving the decimal to the right example: .00945 9.45x10^-3 10-1 = 1/10 = .1 10-2 = 1/100 = .01 10-3 = 1/1,000 = .001

Standard Form If a number is already in scientific notation then we can change it back to standard form. Example: 7.8x 104 would be written 78,000 because we moved the decimal place 4 to the right because of the 4 exponent on top of the 10. 7.8x10-4 would be written .00078 because we moved the decimal place 4 to the left because of the negative 4 on top of the 10.

Convert these numbers to standard notation or scientific notation Lets Practice! Convert these numbers to standard notation or scientific notation 6.17 x104 2.07 x10-3 .00098 139700000 61700 00207 9.8 x10-4 1.397 x108