Significant numbers (figures):
Significant numbers are digits in a number. Leading zeros are not significant numbers.
Measurements have always uncertanities due to limitations of instruments, human error and also
environmental factors. Uncertanity is about how well you know the measurement’s true value.
Uncertanity is indicated by the significant numbers in the measured value.
Number (measured value)
90.2
7.5
7.40
0.054
Significant figures
3
2
3
2
Least significant figure
2
5
0
4
Rounding off: To prevent high precision (precision is about how close measuments are to each
other)
➢ Assume the digit is 8.54: When the least significant number is least than 5, the number
can be rounded down as 8.5
➢ Assume the digit is 8.56: When the least significant number is greater than 5, the number
can be rounded up as 8.6
➢ Assume the digit is 4.48917812:
If you round as 4.5 the precision is 0.1
If you round as 4.49 precision is 0.01
If you round as 4.489 presicion is 0.01 (high precision less uncertainty)
Multiplied or divided:
When the significant numbers are multiplies or divided, the result significant number should be
same as the product which has fewer significant number.
4.236/0.49=8.6448979592 the results should be rounded as 8.6
1st digit has 4 significant number and 2nd digit has 2 significant number.
Added or substracted:
When the numbers are added or substracted, the result uncertainty should be same as the
product which has largest uncertainty.
8.1+3.77= 11.87 the result should be rounded as 11.9 (the result uncertainty is 0.1)
Uncertanity of 1st digit is (0.1) and uncertainty of 2nd digit is (0.01).