Question

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8. Round the following: a. \( 2.4568 \mathrm{mg} \) (to the nearest tenth) b. \( 0.5478 \mathrm{mcg} \) (to the nearest hundredth) c. \( 3.175 \mathrm{mg} \) (to the nearest hundredth) 9. Convert the

Answer 1

Rounding numbers to the indicated number of significant figures is essential for precision. Example a rounds to 0.42, b rounds to 0.00387, c rounds to 421.3, and d stays as 28,683. Remember to match the precision when multiplying or dividing.

Step-by-step explanation:

Rounding numbers to the indicated number of significant figures is an important concept in mathematics, especially when dealing with measurements and precision. Here are examples with explanations:

• a. To round 0.424 to two significant figures, we look at the third figure (4) and see that it is less than 5, so we do not increase the second figure. The result is 0.42.
• b. To round 0.0038661 to three significant figures, the fourth figure (6) is 5 or more, so we round up the third figure to 7, giving us 0.00387.
• c. Rounding 421.25 to four significant figures, we look at the fifth figure which is absent; hence, no rounding is needed. The result is 421.3.
• d. To round 28,683.5 to five significant figures, the figure after the fifth figure is less than 5, so the number remains 28,683.

When rounding numbers for multiplication and division, follow the rule of rounding the result to the same number of significant figures as the number with the fewest significant figures. This ensures the precision of the result is not overstated.