1/27/09
Post date: Jan 26, 2009 9:29:54 PM
Bell Ringer: Why do we use significant digits in science?
Arithmetic with scientific notation
In order to add or subtract, we must first have common exponents for the x 10^n .
If n's are the same for each, add or subtract the M values and keep the "x 10^n" at the end
If n's are different, move the decimal in the M value until you have a common n for each, then add or subtract the M's.
To multiply
Multiply the M values to get the M for your product
Add the n values to the get the n for your product
To divide
Divide your M values to get the M for your quotient
Subtract your n values to get the n for your quotient
Pages 18-19: 7-10 in your notebook for practice
Significant Digits
Related to precision of the measuring tool
Page 23 - picture describing need for significant digits
Rules
Non-zero digits are ALWAYS significant
All final zeroes after the decimal are significant
Zeroes between other significant digits are significant
Zeroes used only for spacing the decimal are NOT significant
Example problems
251.38 --> All are non-zeroes, so 5 sig digs
1001 --> Two zeroes are between sig digs, so 4 sig digs
0.00240 --> 2 and 4 are sig., final zero after decimal is sig, other zeroes are only spacing the decimal, so 3 sig digs
Do page 24: 12-13 (only a-c for each)
Scientific notation ONLY shows sig digs (eliminates 0 confusion)
e.g. 251.30 --> 2.5130 x 10^2
e.g. 1001 --> 1.001 x 10^3
e.g. 0.00240 --> 2.4 x 10^-3
For the problems you did earlier, write each number in scientific notation
Operations with significant digits
Addition or subtraction
Round to the same decimal as the least precise measurement
e.g. 1.2 + 3.41 + 12.02 = ?
1.2 is rounded to the tenths place, so answer must be rounded to tenths place
1.2+3.41+12.02=16.63, but rounded to the tenths is 16.6
Multiplication or Division
Answer has same number of sig digs as the measurement with the fewest sig digs
e.g. 3.0 x 14.125
3.0 has 2 sig digs, 14.125 has 5 sig digs, so answer must have 2 sig digs
3.0 x 14.125 = 42.375
round to 2 sig digs, so answer is 42
Do page 25: 14-17
Add to previous problems
Due Wednesday, 1/28/09