Ch.1 - Matter, Measurement & Problem Solving

Problem 57a,b,c

Chapter 1, Problem 57a,b,c

Use scientific notation to express each quantity with only base units (no prefix multipliers). a. 4.5 ns b. 18 fs c. 128 pm

Verified step by step guidance

Identify the given quantity: 128 pm (picometers).

Recall that 1 picometer (pm) is equal to 10^{-12} meters (m).

Convert the given quantity from picometers to meters by multiplying: 128 pm \times 10^{-12} m/pm.

Express the result in scientific notation by adjusting the decimal point and the exponent accordingly.

Ensure the final expression is in the form of a single digit before the decimal point followed by the appropriate power of ten.

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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 method of expressing numbers as a product of a coefficient and a power of ten. It simplifies the representation of very large or very small numbers, making calculations easier. For example, the number 128 can be expressed as 1.28 x 10^2 in scientific notation.

Unit Conversion

Unit conversion involves changing a quantity expressed in one unit to another unit. In this case, converting picometers (pm) to meters (m) is necessary, as scientific notation should only use base units. Since 1 pm equals 1 x 10^-12 m, the conversion is essential for accurate representation.

Base Units

Base units are the fundamental units of measurement in the International System of Units (SI). They include meters, kilograms, seconds, etc. When expressing quantities in scientific notation, it is important to use these base units to maintain consistency and clarity in scientific communication.

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