Significant Figures (Lecture 5)

Question 1

Significant figures

Answer 1

The number of significant figures is the minimum number of digits needed to write a given value in scientific notation without loss of precision.
The significant figures of a number are digits that carry meaning contributing to its measurement resolution.

Question 2

When are zeros significant?

Answer 2

• in the middle of a number
• at the end of a number on the right-hand side of a decimal point.
• non zero digits are always significant

Question 3

How do significant figures work in addition and subtraction?

Answer 3

• If the numbers to be added or subtracted have equal numbers of digits, the answer goes to the same decimal place as in any of the individual numbers.
• The number of significant figures in the answer may exceed or be less than that in the original data.
• If the numbers being added do not have the same number of significant figures, we are limited by the least certain one.

Question 4

How do significant figures work in multiplication and division?

Answer 4

• We are limited to the number of significant figures contained in the number with the fewest significant figures.

Question 5

How do significant figures work in logarithms and anti-logarithms?

Answer 5

• The number of digits in the mantissa (after decimal point) of log n should equal the number of significant figures in n.
• In the conversion of a logarithm into its antilogarithm, the number of significant figures in the antilogarithm should equal the number of digits in the mantissa.