Correct any answers that have the incorrect number of...

Correct any answers that have the incorrect number of significant figures. (a) $34.00 \times 567 \div 4.564=4.2239 \times 10^{3}$ (b) $79.3 \div 0.004 \times 35.4=7 \times 10^{5}$ (c) $89.763 \div 22.4581=3.997$ (d) $\left(4.32 \times 10^{12}\right) \div\left(3.1 \times 10^{-4}\right)=1.4 \times 10^{16}$

Correct any answers that have the incorrect number of significant figures.
(a) $34.00 \times 567 \div 4.564=4.2239 \times 10^{3}$
(b) $79.3 \div 0.004 \times 35.4=7 \times 10^{5}$
(c) $89.763 \div 22.4581=3.997$
(d) $\left(4.32 \times 10^{12}\right) \div\left(3.1 \times 10^{-4}\right)=1.4 \times 10^{16}$

Key Concepts

Rounding

Rounding is the process of adjusting a numerical value to a specified degree of precision, often determined by the number of significant figures. In the context of significant figures, rounding is used to ensure that the final result carries the proper level of precision based on the inputs. Proper rounding techniques prevent the communication of misleading precision in calculated outcomes.

Scientific Notation

Scientific notation expresses numbers as a product of a coefficient and a power of ten, which is especially useful for very large or very small numbers. When using scientific notation, it is important that the coefficient is rounded to the appropriate number of significant figures, maintaining consistency with the precision rules of significant figures in calculations.

Significant Figures

Significant figures are the digits in a number that carry meaning regarding its precision. They include all non-zero digits, any zeros between them, and sometimes trailing or leading zeros when they are significant based on the context or notation. Maintaining the appropriate number of significant figures in an answer reflects the precision of the measurements used in calculations.

Arithmetic Operations with Significant Figures

When performing multiplication and division, the result should be rounded off to the same number of significant figures as the operand with the fewest significant figures. This rule helps ensure that the final answer does not imply a greater precision than the measurements allow. It is critical to identify the operand with the smallest number of significant figures to correctly round the computed result.

Transcript

Please give Ace some feedback