# Number of significant figures in 5*5.364

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• Elena14
In summary, if the number 5 is itself a measurement, then use rule 2. If 5 is a pure number, then use rule 1.
Elena14
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??

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. :-(

Last edited:
brotherStefan said:
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.

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.

## 1. How do you determine the number of significant figures in 5*5.364?

The number of significant figures in a product is equal to the number of significant figures in the factor with the least number of significant figures. In this case, 5 has only one significant figure, so the answer will also have one significant figure.

## 2. Why is it important to consider significant figures in calculations?

Significant figures represent the precision of a measurement or calculation. Including the correct number of significant figures ensures that the result is accurate and not misleading.

## 3. What is the significance of the number of significant figures in scientific measurements?

The number of significant figures indicates the level of precision and uncertainty in a measurement or calculation. It is important to report measurements with the correct number of significant figures to accurately represent the data.

## 4. Do all numbers in a calculation contribute to the number of significant figures in the result?

No, only the numbers that are significant themselves contribute to the significant figures in the result. Zeros may or may not be significant, depending on their placement in the number.

## 5. How can I determine the number of significant figures in a decimal number?

In a decimal number, all non-zero digits are significant. Zeros at the beginning or end of a number are not significant, but zeros between non-zero digits are significant.

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