Perform the following mathematical operation, and report the answer to the correct number of significant figures.
[tex]0.0016 \div 0.849=[?][/tex]
Answer (2)
The result of dividing 0.0016 by 0.849 is approximately 0.00188456 , which is rounded to 0.0019 to reflect the correct number of significant figures, which is 2. Thus, the final answer is 0.0019 .
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Divide 0.0016 by 0.849, resulting in approximately 0.00188456.
Determine the number of significant figures in each number: 0.0016 has 2, and 0.849 has 3.
Round the result to the smallest number of significant figures, which is 2.
The final answer, rounded to 2 significant figures, is 0.0019 .
Explanation
Understanding the Problem We are asked to perform the division 0.0016 o b re ak o in d e n t \[ 0.2 c m ] o b re ak o in d e n t ÷ 0.849 and report the answer to the correct number of significant figures.
Performing the Division First, let's perform the division:
0.0016 o b re ak o in d e n t \[ 0.2 c m ] o b re ak o in d e n t ÷ 0.849 = 0.00188456...
Significant Figures Now, we need to consider significant figures. The number 0.0016 has two significant figures (the 1 and the 6), while the number 0.849 has three significant figures (8, 4, and 9). When dividing, the result should be rounded to the same number of significant figures as the number with the fewest significant figures. In this case, that's two significant figures.
Rounding the Result Rounding 0.00188456... to two significant figures, we look at the first two non-zero digits, which are 1 and 8. The next digit is 8, which is greater than or equal to 5, so we round the 8 up to a 9. Therefore, the result rounded to two significant figures is 0.0019.
Final Answer Therefore, 0.0016 o b re ak o in d e n t \[ 0.2 c m ] o b re ak o in d e n t ÷ 0.849 = 0.0019 when rounded to the correct number of significant figures.
Examples
Significant figures are important in scientific calculations to accurately represent the precision of measurements. For example, if you are calculating the density of a substance by dividing its mass (measured as 0.0016 grams) by its volume (measured as 0.849 mL), you would need to report the density as 0.0019 g/mL to reflect the precision of your measurements. Reporting more digits would imply a higher level of precision than is actually present in your initial measurements.
