# Confusion regarding significant figures in answers

• fleetingmoment
In summary, the conversation is about a student working on converting units of speed from SI units to other units. They are confused about significant figures and how they should be expressed in the answer. The conversation ends with the student realizing their mistake and understanding that the answer should have the same number of significant figures as the term with the least number of significant figures in the question.
fleetingmoment

## Homework Statement

I'm working through some exercises in which I'm supposed to convert various units of speed from SI units to other units
Example: 0.4m/s into km/h

## The Attempt at a Solution

Having checked, I know my answer to be (to 3 significant figures) correct. My confusion arises regarding significant figures. Wouldn't 0.4 be 1 significant figure, which, if I remember and understand correctly, influences how the answer must be expressed, which in turn would leave me with a answer value of 1.

Doesn't the exercise state explicitly how many significant figures are needed for the result?

fleetingmoment said:

## Homework Statement

I'm working through some exercises in which I'm supposed to convert various units of speed from SI units to other units
Example: 0.4m/s into km/h

## Homework Equations

View attachment 112152

## The Attempt at a Solution

Having checked, I know my answer to be (to 3 significant figures) correct. My confusion arises regarding significant figures. Wouldn't 0.4 be 1 significant figure, which, if I remember and understand correctly, influences how the answer must be expressed, which in turn would leave me with a answer value of 1.

It's okay. I worked out where I was going wrong.

fleetingmoment said:
It's okay. I worked out where I was going wrong.
did you get the answer? when you are multiplying 2(or more) terms, the answer should contain as much as significant figures which is equivalent to that of the least number of significant figures containing term in the question.

harini07 said:
did you get the answer? when you are multiplying 2(or more) terms, the answer should contain as much as significant figures which is equivalent to that of the least number of significant figures containing term in the question.
oops sorry, just now i have seen that it's marked solved.ignore my useless rambling then :p

## 1. What are significant figures and why are they important?

Significant figures are digits in a numerical value that represent the precision of a measurement or calculation. They are important because they help to convey the accuracy and reliability of a number.

## 2. How do I determine the number of significant figures in a measurement?

The general rule is that all non-zero digits are significant, while zeros may or may not be significant depending on their placement. Zeros at the beginning of a number are not significant, zeros between non-zero digits are significant, and zeros at the end of a number after a decimal point are significant. There are also specific rules for numbers written in scientific notation.

## 3. What is the significance of rounding when dealing with significant figures?

Rounding is important in order to maintain the correct number of significant figures in a calculation or measurement. When rounding, the final digit should be rounded up if it is 5 or higher, and rounded down if it is 4 or lower.

## 4. Can significant figures be used in mathematical operations?

Yes, significant figures should be used in mathematical operations to maintain the same level of precision in the final answer. The result of a calculation should have the same number of significant figures as the number with the fewest significant figures used in the calculation.

## 5. How do significant figures affect the reporting of scientific data?

Significant figures are crucial in the accurate reporting of scientific data. They help to convey the precision and reliability of the data, and also ensure that the data is consistent and comparable among different researchers or experiments.

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