Transcript significant figures - New York Science Teacher

WHAT IS A SIGNIFICANT
FIGURE?
When you are making a measurement there are
always a certain number of known or certain digits.
Then as part of the measurement there will always
be a digit that is uncertain because it is your guess.
The known or certain digits plus the first unknown
Digit is referred to as the SIGNIFICANT FIGURES
Kenneth E. Schnobrich
PRECISION vs ACCURACY
PRECISION: this refers to a situation where the same
result is gotten each time you perform the operation
• repeatedly hitting the same spot in darts
ACCURACY: this refers to how close you come to
the accepted value or result
• how close you are to the bullseye
SIGNIFICANT FIGURES
The following rules apply to significant figures:
1. All digits in a measurement are considered significant
2. Zeros that fall between digits are considered
significant
3. Zeros to the right of a decimal and to the right of a
non-zero are considered significant
4. If a decimal point is placed after a zero all of the
intervening zeros are significant
5. Zeros after a digit but not followed by a decimal are
not significant
EXACT NUMBERS
These are usually numbers that are obtained by
counting rather than using a measuring device
such as a buret or graduated cylinder - 12 eggs in
dozen, 2 socks in a pair, 144 in a gross
© Kenneth E. Schnobrich
SIGNIFICANT FIGURES
Working with Significant figures:
1. When you add or subtract numbers:
the final answer can have no more decimal
places than the least precise value in the operation
2. When you multiply or divide numbers:
the final answer can have no more significant
figures than the smallest number of significant
figures in the operation
EXAMPLES
ADDING & SUBTRACTING:
5.0043
5.0043
4.032
1.02
1.02
4.02
3.2
13.3
EXAMPLES
Multiplying and Dividing
4.91
5.0043
4.032
20.33
1.02
5.0043
MORE EXAMPLES
How many Significant figures in each of the following:
1. 0.0043
2. 1.0043
3. 14300
4. 5820.
5. 30089
6. 2.0607
MORE EXAMPLES
How many Significant figures in each of the following:
1. 243.0 x 1.8 =
2. 1.0043 + 2.08 =
3. 14300/4 =
4. 5820. x 4.32 =
5. 30089 - 7.32 =
6. 2.0607 + 3.85 =
ROUNDING
When rounding use only the first digit to the right of the last
significant figure . 4.348 becomes 4.3 if rounded to 2 sig.figs.
Rules:
-In a series of calculations, carry the extra digits through to the
final result, then round.
-If the digit to be removed
-Is less than 5 the preceding digit stays the same. 1.33
becomes 1.3
-Is equal to or greater than 5, the preceding digit is increased
by 1. 1.36 becomes 1.4