Physics
Physics
Problem
Three physical quantities are given as , and (all in consistent units). (i) Multiply the three quantities and obtain the unnormalised product. (ii) Rewrite the product obtained in part (i) in proper scientific notation. (iii) Apply the rule of significant figures to report the final answer correctly.Intuitive explanation
When multiplying numbers in scientific notation, you're really multiplying two things separately: the decimal coefficients and the powers of 10. The key insight is that significant figures—the digits you can trust—come from your least precise measurement, so your final answer can't claim more precision than your weakest input. After combining everything mathematically, you'll need to round to match the smallest number of significant figures among your three original quantities.
Intuitive explanation
When multiplying numbers in scientific notation, you're really multiplying two things separately: the decimal coefficients and the powers of 10. The key insight is that significant figures—the digits you can trust—come from your least precise measurement, so your final answer can't claim more precision than your weakest input. After combining everything mathematically, you'll need to round to match the smallest number of significant figures among your three original quantities.