# Error and significant figures when rounding?

• bingoboy
In summary, the conversation is about determining the specific heat capacity of brass for a lab report. The initial temperature measurement was to two significant figures and the final answer was 0.38 (j/g*K) with an error of 0.0235. The error was rounded to two significant figures, resulting in an answer of 0.38±0.024. The question then arises whether the error should be rounded to the hundredths place or left as it is. The response is that the error should be rounded to 0.02.
bingoboy

## Homework Statement

So I'm determining the specific heat capacity of brass for a lab report, when i initially measured temperature it was to two significant figures (this was the measurement with the least significant figures)

My final answer, remarkably was 0.38 (j/g*K) but my error was 0.0235 so i rounded that to two significant figures, however doing that i get an answer of 0.38±0.024. This means that my highest and lowest measured value would be to three significant figures (0.38-0.024=0.356 (j/g*K)) see my problem?

## The Attempt at a Solution

Should i round the error to the hundredths place or should i just leave my error as it is?

You think it correctly, the error has to be rounded to 0.02.

ehild

## What is rounding error and why is it important?

Rounding error refers to the difference between the exact value of a number and the rounded version of that number. It is important because it can affect the accuracy and precision of calculations, especially in scientific research where precise measurements are crucial.

## What are significant figures and how do they relate to rounding?

Significant figures are the digits in a number that are known with certainty plus one estimated digit. When rounding a number, the number of significant figures determines how many digits after the decimal point should be kept or discarded.

## How do you determine which digit to round up or down when using significant figures?

When using significant figures, if the digit to the right of the last significant figure is 5 or greater, the last significant figure is rounded up. If the digit is less than 5, the last significant figure remains the same. If the digit is exactly 5, the last significant figure is rounded up if it is odd and remains the same if it is even.

## What is the difference between rounding to a specific number of decimal places and rounding to a specific number of significant figures?

Rounding to a specific number of decimal places means the number will have that exact number of digits after the decimal point, while rounding to a specific number of significant figures means the number will have that exact number of significant figures, regardless of the decimal places. Rounding to significant figures preserves the accuracy of the measurement, while rounding to decimal places can introduce errors.

## How do you handle rounding when performing mathematical operations?

When performing mathematical operations, it is important to keep track of significant figures and round the final answer to the appropriate number of significant figures. If the numbers being operated on have different numbers of significant figures, the final answer should be rounded to the least number of significant figures.

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