· There are two kinds of numbers in scientific work: exact numbers and inexact numbers.
· Exact numbers have defined values.
· Inexact numbers are values that have uncertainty; numbers obtained by measurements are always inexact.
· Precision is a measure of how closely individual measurements agree with one another.
· Accuracy refers to how closely individual measurements agree with the correct value.
· Consistent measurements are precise but may be inaccurate due to an error in the instrument used.
· Measured quantities are displayed in a way that leaves only the last digit uncertain.
· Significant figures are all digits in a measured quantity, including the uncertain one.
· There are three rules for determining the number of significant digits:
1) Zeros between nonzero digits are always significant.
2) Zeros to the left of the number are not significant and are only used to locate the decimal point.
3) Zeros to the right of the number are significant if the number contains a decimal point.
- Examples: 0.0034 has two significant figures; 1240 has four; 201.454 has six.
- Example: 152,000 has six significant figures; when it is written in scientific notation, 1.52 x 105, it has three.
- When making calculation, the last certain measurement limits the certainty of the calculated quantity.
- The least certain measurement determines the number of significant figures in the final answer.
- When multiplying or dividing, the product or quotient must contain the same number of significant figures as the measurement with the fewest significant figures.
- Example: 45.6 x 1.342 = 61.1952, the answer is rounded to three significant figures, 61.2, because 45.6 is the number with the least significant figures.
- When adding or subtracting, the sum or difference has the same number of decimal places as the measurement with the fewest decimal places.
- Example: 1023.2 + 2.34 = 1025.54, the answer is rounded to one decimal place, 1025.5, because 1023.2 has the least number of decimal places.
No comments:
Post a Comment