Calculate to the correct number of significant figures. d. (1.128x10⁵) / (2.7x10²)

Verified step by step guidance

1. Identify the number of significant figures in each number: 1.128x10^5 has 4 significant figures and 2.7x10^2 has 2 significant figures.
2. Perform the division: (1.128x10^5) / (2.7x10^2).
3. Calculate the result of the division without rounding yet.
4. Determine the number of significant figures for the final answer: it should have the same number of significant figures as the number with the fewest significant figures in the original problem, which is 2.
5. Round the calculated result to 2 significant figures to obtain the final answer.

Key Concepts

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. When performing calculations, the result should be reported with the same number of significant figures as the measurement with the least number of significant figures.

Division in Scientific Notation

When dividing numbers in scientific notation, you divide the coefficients and subtract the exponents of the powers of ten. For example, in the expression (1.128x10^5) / (2.7x10^2), you would first calculate 1.128 / 2.7 and then adjust the exponent by subtracting 2 from 5, resulting in a new scientific notation format.

Rounding Rules

Rounding rules dictate how to adjust numbers to reflect the correct number of significant figures. If the digit to be dropped is less than 5, the last retained digit remains unchanged; if it is 5 or greater, the last retained digit is increased by one. This ensures that the final answer is both accurate and appropriately precise.