Perform each calculation to the correct number of...

Perform each calculation to the correct number of significant figures.
(a) $4.5 \times 0.03060 \times 0.391$
(b) $5.55 \div 8.97$
(c) $\left(7.890 \times 10^{12}\right) \div\left(6.7 \times 10^{4}\right)$
(d) $67.8 \times 9.8 \div 100.04$

Key Concepts

Significant Figures

Significant figures represent the digits in a number that contribute to its precision. They include all certain digits plus one uncertain or estimated digit. Understanding significant figures is crucial in science and engineering to correctly express the uncertainty in measured or calculated values.

Rules for Multiplication and Division

When performing multiplication or division, the result should have the same number of significant figures as the measurement with the fewest significant figures. This rule ensures that the precision of the final result does not exceed that of the least precise measurement involved in the calculation.

Rounding Techniques

Rounding is used to adjust a number so that it has the correct number of significant figures. This process involves identifying the digit at the required level of precision and then determining whether to round up or down based on the value of the subsequent digit, ensuring that the reported value accurately reflects the measurement's precision.

Scientific Notation

Scientific notation is a way of expressing numbers as a product of a coefficient and a power of ten, which is particularly useful for handling very large or very small numbers. In the context of significant figures, the coefficient is where the significant digits are found, so it's important to correctly count and round these digits when performing calculations.

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