# Significant Figures in Conversion Factors

• Jordan Bergeron
In summary, when converting between units, the number of significant figures in the final answer should be based on the unit with the smallest number of significant figures. This explains why in the examples given, the number of significant figures varies. Additionally, for exact conversion factors, such as fathoms to feet, the conversion factor has an infinite number of significant figures. Rules for significant figures in addition and subtraction also depend on the location of the decimal point.
Jordan Bergeron
So from what I had initially understood, in a conversion problem, you go by whatever number has the smallest SF and round your answer to that number, even if that number is one.

In the examples on my homework it seems like my teacher chooses a random number of significant figures for each problem and I can't figure out why.

Some Examples:
2425 fathoms x(6 ft/1 ft)x(12 in/ 1 ft)x(2.54 cm/in)x(1 m/100 cm)= 4435 m
-Why not 1, 2 or even 3 SF?

20.0 inx(2.54/1 in)x(1 m/ 100 cm)x(1000 mm/ 1 m)= 508 mm
-Why not 1 SF?

15.4-11= 4
-Why not 2 SF?

Fathom is by definition EXACTLY 6 feet, so the conversion factor has an infinite number of digits. Same about inch vs cm.

Rules for addition and subtraction are slightly different and result depends on where the decimal point is.

## 1. What are significant figures in conversion factors?

Significant figures are digits in a number that are considered to be accurate and reliable. They indicate the precision of a measurement or calculation. In conversion factors, significant figures are used to determine the accuracy of the converted value.

## 2. How do significant figures affect conversion factors?

Significant figures are important in conversion factors because they determine the number of digits that should be included in the converted value. The converted value should have the same number of significant figures as the original value, in order to maintain accuracy and precision.

## 3. Can significant figures be used in all types of conversion factors?

Yes, significant figures can be used in all types of conversion factors. Whether it is a simple conversion between units of measurement or a more complex conversion involving multiple units, significant figures are essential in ensuring the accuracy of the converted value.

## 4. How do you determine the number of significant figures in a conversion factor?

The number of significant figures in a conversion factor is determined by the original value. Count the number of digits in the original value, starting from the first nonzero digit. All digits are considered significant, except for trailing zeros after a decimal point. For example, in the conversion factor 2.54 cm = 1 in, there are three significant figures.

## 5. What happens to significant figures when multiplying or dividing using conversion factors?

When multiplying or dividing using conversion factors, the number of significant figures in the final answer should be equal to the least number of significant figures in the original values. For example, if one value has 3 significant figures and the other has 2 significant figures, the final answer should have 2 significant figures.

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