Title: Accuracy, Precision, Signficant Digits and Scientific Notation
1Accuracy, Precision, Signficant Digits and
Scientific Notation
2Accuracy and Precision
- Accuracy refers to how close a given quantity
is to an accepted or expected value (page 19) - Precision refers to how exact a measurement is.
It also refers to how close measurements are to
each other (see page 16 and 19)
3Example
4Watch the following video clip
5Rules for Significant Digits
- Digits from 1-9 are always significant.
- Zeros between two other significant digits are
always significant - One or more additional zeros to the right of both
the decimal place and another significant digit
are significant. - 4. Zeros used solely for spacing the decimal
point (placeholders) are not significant.
6Examples of Significant Digits
7Multiplying and Dividing
- RULE When multiplying or dividing, your answer
may only show as many significant digits as the
multiplied or divided measurement showing the
least number of significant digits
8Example When multiplying 22.37 cm x 3.10 cm x
85.75 cm 5946.50525 cm3We look to the
original problem and check the number of
significant digits in each of the original
measurements 22.37 shows 4 significant
digits.3.10 shows 3 significant digits.85.75
shows 4 significant digits.Our answer can only
show 3 significant digits because that is the
least number of significant digits in the
original problem. 5946.50525 shows 9 significant
digits, we must round to the tens place in order
to show only 3 significant digits. Our final
answer becomes 5.95 x 103 cm3.
9Scientific Notation
- Use this method to express large numbers and
doing calculations by using powers of 10 - To do this, count the number of places you have
to move the decimal point to yield a value
between 1 and 10. This counted number is the
exponent. The exponent is positive if the
original number is greater than 10 and negative
if the original number is less than 10 - Examples
- 150 000 000 000 is 1.5 x 1011m
- 0.000 000 000 050 is 5.0 x 10-11m
10Adding and Subtracting
- RULE When adding or subtracting your answer can
only show as many decimal places as the
measurement having the fewest number of decimal
places.
11Example When we add 3.76 g 14.83 g 2.1 g
20.69 gWe look to the original problem to see
the number of decimal places shown in each of the
original measurements. 2.1 shows the least
number of decimal places. We must round our
answer, 20.69, to one decimal place (the tenth
place). Our final answer is 20.7 g
12Practice sig figs
13Practice Adding and substracting
14Practice Multiplying and dividing
15Rounding Rules
- If your answer ends in a number greater than 5,
increase the preceding digit by 1. - Example 2.346 can be rounded to 2.35
- 2. If your answer end with a number that is less
than 5, leave the preceding number unchanged - Example 5.73 can be rounded as 5.7
16Rounding rules continued
- 3. If you answer ends with 5, increase the
preceding number by 1 if it is odd. Leave the
preceding number unchanged if it is even. - For example, 18.35 can be round to 18.4, but
18.25 is rounded to 18.2