Transcript Slide 1

Scientific Notation
• Add and Subtract – make the
powers the same, add the
numbers and keep powers as
they are.
Scientific Notation
• Multiply – multiply numbers
and add exponents
Scientific Notation
• Multiply – multiply numbers
and add exponents
• Divide – multiply numbers and
subtract exponents
Significant figures
All non-zero digits are significant
15, 699 (Five sig. figs)
Significant figures
Zeros to the left of the first non-zero digit
are not significant
(these are called leading zeros)
0.23 (Two sig figs) 0.00023 (Two sig. figs)
Significant figures
Zeros between non-zero
digits are significant
(these are called captive zeros)
7077 (Four sig. figs) 50.2 (Three sig. figs)
Significant figures
Zeros at the end of a number that
includes a decimal point are significant
(these are called trailing zeros)
50.020 (Five sig. figs)
Significant figures
For numbers with a zero (or zeros) at the end
and no decimal point, it is impossible to know
how many of the digits are significant. e.g.
consider 100: Does this measurement have one,
two or three sig. figs? Written in this fashion,
there is no way to tell. We can get around this
problem by using scientific notation; with
scientific or exponential notation, the numbers
written down are always significant
1.00 x102 (Three sig. figs) 1. x102 (One sig. fig.)
Multiplication or Division
The result of multiplication or division can
contain only as many sig. figs as the least
precisely known quantity in the calculation.
4.93 x 3.1 = 15.28 = 15 (Two sig. figs)
100.00 + 40 = 2.5 = 3 (One sig. fig)
Addition or Subtraction
The number of decimal places in the
answer must be the number with the
lowest precision in the group of
numbers that are added or subtracted.
4.00 + 2.0 = 6.0
9.42 + 6.7 + 3.3 =19.4