Perform the following mathematical operation, and report the answer to the correct number of significant figures.
[tex]$9.635 \div 12.9=$[/tex]
Answer (2)
To find the result of 9.635 divided by 12.9 , first perform the division to get approximately 0.7469 . Since 12.9 has the fewest significant figures (three), round the result to three significant figures, giving us a final answer of 0.747 .
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Divide 9.635 by 12.9 to get 0.7468992248062015.
Identify that 9.635 has four significant figures and 12.9 has three significant figures.
Round the result to three significant figures.
The final answer is 0.747 .
Explanation
Understanding the Problem We are asked to perform the division 9.63512.9 and report the answer to the correct number of significant figures. The number 9.635 has four significant figures, and the number 12.9 has three significant figures. Therefore, the result of the division should be rounded to three significant figures.
Performing the Division Performing the division, we get 9.63512.9 = 0.7468992248062015
Rounding to Correct Significant Figures Since we need to round the result to three significant figures, we look at the first four digits: 0.7468. Since the fourth digit is 8, which is greater than or equal to 5, we round up the third digit. Thus, 0.7468 becomes 0.747.
Final Answer Therefore, the final answer, rounded to three significant figures, is 0.747.
Examples
Significant figures are important in scientific calculations to accurately represent the precision of measurements. For example, if you are measuring the speed of a car using a radar gun, and the radar gun is accurate to three significant figures, then you should report the speed of the car to three significant figures. If the radar gun reads 25.6789 mph, you should report the speed as 25.7 mph. This indicates that you are confident about the first three digits, but the remaining digits are uncertain.
