Question

Round each to three significant figures.

1) Part A. 79900
2) Part B. 1.57 ×10⁷
3) Part C. 2.35
4) Part D. 0.0000454

Answer 1

The numbers 79900, 1.57×10⁷, 2.35, and 0.0000454 when rounded to three significant figures remain the same except for the last one, which still has three significant figures when considering the first non-zero digit. The correct answer is 1)

Step-by-step explanation:

To round the given numbers to three significant figures, we can follow these simple steps for each number:

1. For 79900, we consider the first three non-zero digits which gives us 799. Since the next digit is zero, we remain with 799 and add the zeroes to get the same power of 10, so the rounded number is 79900 (7.99×10´ in scientific notation).
2. The number 1.57 ×10⁷ is already in scientific notation with three significant figures, so no rounding is necessary. The rounded number remains 1.57 ×10⁷.
3. For 2.35, since it already has three significant figures, no rounding is required. Therefore, the rounded number is 2.35.
4. The number 0.0000454 has three significant figures, but we need to consider significant figures starting from the first non-zero digit. Thus, we get 4.54 (since '454' have three significant figures). Translating this back to the original decimal form, we will keep three significant figures, resulting in 0.0000454.

In rounding, significant figures play a crucial role in determining the precision of reported numbers in scientific and mathematical contexts. In each case above, the numbers are adjusted to reflect three significant digits, which is a common requirement in many scientific calculations.