Question
In a measurement, you calculate its measured value to be 21.953643290pm 5.3326435 How should you write down its average value as an answer?
Solution
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YorkElite · Tutor for 8 years
Answer
### $22.0 \pm 5.3$
Explain
## Step 1: Identifying Significant Figures in Uncertainty<br />### The uncertainty $5.3326435$ has two significant figures (determined by the first two digits, 5 and 3, as the first digit after the decimal point is non-zero). We round the uncertainty to two significant figures, resulting in 5.3.<br />## Step 2: Rounding the Measurement<br />### The average value, $21.953643290$, needs to be rounded to the same decimal place as the uncertainty, which is the tenths place. Rounding $21.953643290$ to the tenths place gives $22.0$.<br />## Step 3: Final Representation<br />### The final answer should be written as $22.0 \pm 5.3$. This reflects the precision of the measurement based on the significant figures in the uncertainty.
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