Write each of the following numbers in scientific notation...

Write each of the following numbers in scientific notation to the number of significant figures indicated in parentheses.
a. 0.00300300 (three)
b. 936,000 (two)
c. 23.5003 (three)
d. $450,000,001$ (six)

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Key Concepts

Rounding

Rounding is the process of adjusting a number to limit the number of significant digits, thereby approximating the value while preserving its overall magnitude and importance. When rounding to a specified number of significant figures, the standard rules of rounding are applied to ensure that the result is as close as possible to the original value, maintaining the desired precision.

Scientific Notation

Scientific notation is a method of writing numbers as the product of a coefficient and a power of ten. The coefficient is typically a number greater than or equal to 1 but less than 10, and the power of ten indicates the scale or magnitude of the number. This notation is particularly useful for handling very large or very small numbers in a compact and easily comparable form.

Significant Figures

Significant figures are the digits in a number that carry meaning contributing to its precision. They include all non-zero digits and any zeros that are known to be exact or fall between significant digits. The concept of significant figures is essential in ensuring that numerical calculations and representations reflect the appropriate level of precision, which is especially important in scientific measurements.

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