Round to 3 significant figures. [tex]$74.58$[/tex]
Answer (2)
Identify the first three significant figures: 7, 4, and 5.
Observe the next digit: 8.
Apply the rounding rule: Since 8 is greater than or equal to 5, round 5 up to 6.
State the rounded number: 74.6
Explanation
Understanding Significant Figures We are asked to round the number 74.58 to 3 significant figures. Significant figures are the digits in a number that contribute to its precision.
Identifying Significant Digits The first three significant figures in 74.58 are 7, 4, and 5. The digit immediately to the right of the third significant figure (5) is 8.
Rounding Rule Since the digit to the right (8) is greater than or equal to 5, we round up the third significant figure (5) by one. This means 5 becomes 6.
Final Result Therefore, rounding 74.58 to 3 significant figures gives us 74.6 .
Examples
In a science experiment, you might measure a value as 74.58 grams. However, your equipment might only be accurate to three significant figures. In this case, you would round your measurement to 74.6 grams to accurately reflect the precision of your equipment. This ensures that your reported results do not imply a higher level of accuracy than your tools allow.
To round 74.58 to 3 significant figures, identify the first three significant digits (7, 4, and 5) and look at the next digit (8). Since 8 is greater than 5, round up the last significant digit, resulting in 74.6 . Thus, the final answer is 74.6 .
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