Final answer:
Calculations involving significant figures are essential in chemistry to ensure precision in measurement and calculation reporting. The number of significant figures or decimal places dictates how to round and present the final result properly. Examples like multiplying significant figures and adding decimal places clearly demonstrate how to proceed with such calculations.
Step-by-step explanation:
The subject matter pertains to the significant figures in chemistry calculations. Significant figures are critical for correctly reporting the precision of a measurement or calculation in the sciences, especially in chemistry. Calculations must consider the least precise measurement to accurately convey certainty in results.
For example, when calculating (5.63 × 10²) × (7.4 × 10³), you would do the following: First, consider the number of significant figures in each number (5.63 has three and 7.4 has two), then perform the multiplication, and finally report your answer with the least number of significant figures which is two in this case. Similarly, when summing up numbers like 14.98 + 27,340 + 84.7593, the number of decimal places in the least precise measurement (27,340 which has no decimal places) dictates the number of decimal places in the answer.
Determining the correct number of significant figures often involves rounding, and every digit counts towards the precision of a measurement or calculation. For example, the number 0.00045050 has six significant figures because zeros between non-zero digits and trailing zeros in the decimal portion are significant.