Ch.1 - Matter, Measurement & Problem Solving

Tro - Chemistry: A Molecular Approach 6th Edition

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Tro 6th Edition

Ch.1 - Matter, Measurement & Problem Solving

Problem 58b

Chapter 1, Problem 58b

Use prefix multipliers to express each measurement without exponents. b. 45.9 * 10 - 7 s

Verified step by step guidance

Identify the given measurement: 45.9 \(\times\) 10^{-7} \(\text{s}\).

Recognize that the goal is to express this measurement without using exponents by applying an appropriate prefix multiplier.

Recall that the prefix 'nano' (n) represents \(10^{-9}\), and 'micro' (\(\mu\)) represents \(10^{-6}\).

Determine which prefix multiplier is closest to \(10^{-7}\). Since \(10^{-7}\) is between \(10^{-6}\) and \(10^{-9}\), the 'micro' (\(\mu\)) prefix is the closest.

Convert the measurement by expressing 45.9 \(\times\) 10^{-7} \(\text{s}\) as 4.59 \(\times\) 10^{-6} \(\text{s}\), which can be written as 4.59 \(\mu\)\(\text{s}\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is typically formatted as a product of a number between 1 and 10 and a power of ten. For example, 45.9 * 10^-7 can be rewritten as 0.00000459, which is more manageable for calculations.

Prefix Multipliers

Prefix multipliers are standard prefixes used in the metric system to denote specific powers of ten. Common prefixes include 'nano-' (10^-9), 'micro-' (10^-6), and 'milli-' (10^-3). These prefixes simplify the expression of measurements by allowing scientists to communicate large or small quantities without using exponents.

Unit Conversion

Unit conversion involves changing a measurement from one unit to another while maintaining the same quantity. In the context of the question, converting 45.9 * 10^-7 seconds into a more understandable format using prefix multipliers requires recognizing the appropriate prefix that corresponds to the exponent, which in this case is 'nano-' for seconds.

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Conversion Factors

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