What is the numerical value of [tex]$1.2 \times 1.222$[/tex]? Express your answer using the correct number of significant figures.
Answer (2)
Multiply the two numbers: 1.2 × 1.222 = 1.4664 .
Determine the number of significant figures: 1.2 has two, and 1.222 has four.
Round the result to two significant figures.
The final answer is 1.5 .
Explanation
Understanding the Problem We are asked to multiply two numbers, 1.2 and 1.222, and express the answer using the correct number of significant figures.
Multiplying the Numbers First, let's multiply the two numbers: 1.2 × 1.222 = 1.4664 .
Significant Figures Now, we need to consider significant figures. The number 1.2 has two significant figures, while 1.222 has four significant figures. When multiplying, the result should have the same number of significant figures as the number with the fewest significant figures. In this case, the result should have two significant figures.
Rounding the Result We need to round 1.4664 to two significant figures. The digit in the third significant figure is 6, which is greater than or equal to 5, so we round up the second significant figure. Therefore, 1.4664 rounded to two significant figures is 1.5.
Final Answer The numerical value of 1.2 × 1.222 , expressed using the correct number of significant figures, is 1.5 .
Examples
In a science experiment, you might need to multiply measurements that have different levels of precision. For example, if you measure the length of an object as 1.2 meters and its width as 1.222 meters, you would multiply these values to find the area. However, because the length measurement is only precise to two significant figures, your final answer for the area should also be rounded to two significant figures to accurately reflect the precision of your measurements. This ensures that your reported result does not imply a level of accuracy that your measurements do not support.
The product of 1.2 and 1.222 is calculated to be 1.4664 . Due to significant figures, the final answer, rounded to 2 significant figures, is 1.5 . This ensures the precision of the measurements is accurately represented.
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