Final answer:
The total mass of the paper clips in the box is 4.3×10² milligrams or 4.3×10⁻ grams, calculated by multiplying the mass of one paperclip by the number of paper clips and rounding to the correct number of significant figures.
Step-by-step explanation:
To calculate the total mass of the paper clips in the box, you simply multiply the mass of a single paperclip by the number of paperclips in the box. The mass of one paperclip is given as 6.0×10⁻⁴ milligrams and there are 7.23×10⁴ paper clips in the box.
The multiplication process in scientific notation is done by multiplying the numbers and adding the exponents if the base is the same. In this case, we have:
6.0×10⁻⁴ mg × 7.23×10⁴ = (6.0 × 7.23) × (10⁻⁴ × 10⁴) = 43.38 × 10⁰ mg. Since 10⁰ is equal to 1, we don't need to write it, and we get 43.38 mg for the total mass.
However, we need to consider significant figures. The number of significant figures in the mass of a single paperclip and the number of paperclips are two and four respectively. When we multiply these, we must round the result to the least number of significant figures, which is two in this case. So, the total mass rounded to two significant figures is 4.3×10² mg, or the paper clips' total mass can also be converted to grams as 4.3×10⁻ grams since there are 1,000 milligrams in a gram.