Use a scientific calculator to do the following...

Use a scientific calculator to do the following calculations. Express each answer in scientific notation and to the correct number of significant figures. (a) $9.865 \times 10^{3}+8.61 \times 10^{2}$ (b) $\frac{\left(6.626 \times 10^{23}\right) \times\left(3.00 \times 10^{8}\right)}{4.5 \times 10^{-7}}$ (c) $\frac{5.6200 \times 10^{-9}}{3.821 \times 10^{9}}$ (d) $\frac{4.5600 \times 10^{3}-2.91 \times 10^{1}}{5}$, where the 5 is an exact number

Use a scientific calculator to do the following calculations. Express each answer in scientific notation and to the correct number of significant figures.
(a) $9.865 \times 10^{3}+8.61 \times 10^{2}$
(b) $\frac{\left(6.626 \times 10^{23}\right) \times\left(3.00 \times 10^{8}\right)}{4.5 \times 10^{-7}}$
(c) $\frac{5.6200 \times 10^{-9}}{3.821 \times 10^{9}}$
(d) $\frac{4.5600 \times 10^{3}-2.91 \times 10^{1}}{5}$, where the 5 is
an exact number

Key Concepts

Scientific Notation

Scientific notation is a method of writing numbers that accommodates values too large or too small to be conveniently written in standard decimal notation. It expresses a number as a product of a coefficient (between 1 and 10) and a power of ten, allowing for simpler arithmetic with very large or very small numbers and ensuring clarity in communication of precision.

Significant Figures

Significant figures represent the digits in a number that carry meaningful information about its precision. They are used to indicate the reliability of measurements and ensure that results of computations are not reported with unwarranted precision. This concept is crucial when performing operations and rounding results to reflect the accuracy of the original measurements.

Arithmetic Operations

Arithmetic operations in scientific notation involve techniques for adding, subtracting, multiplying, and dividing numbers expressed as a product of a coefficient and a power of ten. Multiplications and divisions use the laws of exponents, while addition and subtraction require aligning the exponents before the operation. These processes are essential for performing accurate and efficient calculations with numbers in scientific notation.

Rounding Rules

Rounding rules are used to adjust the result of a calculation to the appropriate number of significant figures. This ensures that the final answer reflects the precision of the input values. Understanding and applying these rules correctly is crucial, especially when intermediate calculations may lead to more digits than are justified by the least precise measurement in the problem.

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