Use scientific notation and the laws of exponents to perform...

Use scientific notation and the laws of exponents to perform the indicated operations. Give the result in scientific notation rounded to two significant figures.
$$\frac{\left(1 \times 10^{-3}\right)\left(3.28 \times 10^{6}\right)}{4 \times 10^{7}}$$

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Key Concepts

Scientific Notation

Scientific notation is a method of writing numbers that are too large or too small to be conveniently written in standard decimal form. It expresses numbers as a product of a coefficient (usually between 1 and 10) and a power of ten, making it easier to perform operations like multiplication and division with very large or very small numbers.

Laws of Exponents

The laws of exponents govern the operations on numbers in exponential form. These include rules for multiplying and dividing powers of the same base, such as adding or subtracting their exponents, which simplifies the arithmetic when dealing with numbers expressed in scientific notation.

Significant Figures

Rounding to significant figures involves retaining only the digits that contribute meaningfully to a number's precision. This concept is important in scientific calculations to reflect the accuracy of measurements and to ensure that the reported results do not imply greater precision than the original data.

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