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)
Divide 0.0016 by 0.849, obtaining approximately 0.00188456.
Determine that 0.0016 has two significant figures and 0.849 has three significant figures.
Round the result to two significant figures, which is the least number of significant figures in the original numbers.
The final answer, rounded to two significant figures, is 0.0019 .
Explanation
Understanding the Problem We are asked to perform the division $0.0016
div 0.849$ and report the answer to the correct number of significant figures.
Performing the Division First, let's perform the division.
Calculating the Result The result of the division is approximately 0.00188456.
Determining Significant Figures Now, we need to consider significant figures. The number 0.0016 has two significant figures (the 1 and the 6), and the number 0.849 has three significant figures (8, 4, and 9). When dividing, the result should be rounded to the smallest number of significant figures present in the original numbers, which in this case is 2.
Rounding to Correct Significant Figures Rounding 0.00188456 to two significant figures gives us 0.0019.
Final Answer Therefore, $0.0016
div 0.849 = 0.0019$ when rounded to the correct number of significant figures.
Examples
Significant figures are important in many real-world applications, especially in science and engineering. For example, if you are measuring the dimensions of a rectangular garden to calculate its area, and your measurements are 12.3 meters and 4.5 meters, you would multiply these to get 55.35 square meters. However, since 4.5 has only two significant figures, you must round your answer to two significant figures as well, giving you an area of 55 square meters. This ensures that your calculated result accurately reflects the precision of your measurements. Using the correct number of significant figures prevents you from overstating the accuracy of your calculations.
The division of 0.0016 by 0.849 gives approximately 0.00188456. Rounding this result to two significant figures, we obtain 0.0019. Therefore, the final answer is 0.0019.
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