# Number of significant figures in 5*5.364

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## Main Question or Discussion Point

How many significant figures should be present in the answer of 5*5.364?

1) Addition rule: The result cannot have more digits to the right of the decimal point than either of the original numbers.

2) Multiplication rule: The result must be reported with no more significant figures as there are in the measurement with the few significant figures.

Using rule 1: 5*5.364= 5.364+5.364+5.364+5.364+5.364= 26.82

Ans: 4 significant figures.

Using rule 2 : 5*5.364= 26.82 = 30

Ans : 1 significant figure.

Which one is correct??

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DrClaude
Mentor
It depends where the 5 comes from. If it is itself a measurement, then rule 2 is correct. If it is a pure number, then rule 1 is correct.

For example, if you are calculating the circumference of a circle, $C = 2 \pi r$, $2 \pi$ is exact and the number of significant digits for $C$ is the same as for $r$.

One would use rule 1 when the "5" (in your example) is known to imply a counted value (usually a unitless number). In such a case, the counted value is exact, and therefore is considered to represent an infinite number of significant figures.

Rule 2 would apply if, for example, one were calculating work or torque, where each of the numbers represent a measured value of some sort, each with its own implied precision.

Unfortunately, rule 2 often applies when the exercise is simply arbitrary practice between application of the rule for addition vs. the rule for multiplication. :-(

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One would use rule 1 when the "5" implies a counted value (usually a unitless number). In such a case, the counted value is exact, and therefore is considered to represent an infinite number of significant figures.

Rule 2 would apply if, for example, one were calculating work or torque, where each of the numbers represent a measured value of some sort.
What would you do if nothing is mentioned? My textbook says nothing about what that "5" represents.

DrClaude
Mentor
I would take it to be an exact integer. Otherwise, the notation 5. × 5.364 should have been used.

Taking 5 as integer does get me to the answer in my textbook. Thank you.