How to Determine Significant Figures in Multiplication/Division?

In summary, for a question involving multiplication or division between numbers with different significant figures, the answer should have the same number of significant figures as the number with the least amount of significant figures. However, if the number is an exact value (such as a conversion factor), it should not limit the significant figures in the answer. In the specific example given, the answer would have 1 significant figure.
  • #1
parabolic1
1
0
just a quick question... (not a HW question)

i know that when you do multiplication/division between numbers you take the lowest amount of sig figs of the two and apply it to your answer... HOWEVER:

what would be the answer for a question such as:

0.00420 x 60 = ?

the first part has 3 sig figs, while the second part has 1... although I've heard you don't count whole integers, so would the answer be

0.252 or 0.3 ?

thanks
 
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  • #2
The "60" is ambiguous. For example if you are converting from minutes to seconds, 60 is exact, so it has to be treated as having infinite significant digits. To answer your question you need more context.
 
  • #3
Since there's no decimal point with the '60', it has 1 significant digit.
 
  • #4
Andy Resnick said:
Since there's no decimal point with the '60', it has 1 significant digit.

On the other hand, if the 60 is meant to be a conversion factor (i.e, between minutes and seconds, or hours and minutes), then it is to be treated as an exact number that doesn't limit the significant figures.

But yes, if it's just part of the data then 1 significant figure, definitely.
 

Related to How to Determine Significant Figures in Multiplication/Division?

What are significant digits and why are they important?

Significant digits, also known as significant figures, are the digits in a number that are considered to be reliable and accurate. They are important because they help convey the precision and accuracy of a measurement or calculation.

How do I determine the number of significant digits in a number?

To determine the number of significant digits in a number, start from the left and count all the non-zero digits. These are always significant. Then, count any zeros between non-zero digits. These are also significant. Finally, any zeros to the right of the decimal point and after a non-zero digit are significant only if they are explicitly shown to be so.

What are the rules for rounding off numbers with significant digits?

The general rule for rounding off numbers with significant digits is to round to the same number of significant digits as the number with the least amount of significant digits in the calculation. If the digit to be dropped is less than 5, the preceding digit remains unchanged. If the digit to be dropped is 5 or greater, the preceding digit is increased by 1.

Can I add or subtract numbers with different numbers of significant digits?

No, when adding or subtracting numbers, the result should have the same number of decimal places as the number with the least amount of decimal places. This means that you may need to round the numbers to the appropriate number of decimal places before adding or subtracting.

How do I multiply or divide numbers with significant digits?

When multiplying or dividing numbers, the result should have the same number of significant digits as the number with the least amount of significant digits. If the number with the least amount of significant digits has a decimal, then the result should also have the same number of decimal places. If it does not have a decimal, then the result should be rounded to the appropriate number of significant digits.

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