Ch.1 - Chemical Tools: Experimentation & Measurement

Problem 43

Chapter 1, Problem 43

Which quantity in each of the following pairs is larger?(a) 5.63 * 106 cm or 6.02 * 101 km

Verified step by step guidance

Convert both quantities to the same unit for comparison. In this case, convert kilometers to centimeters.

Recall that 1 kilometer (km) is equal to 100,000 centimeters (cm).

Convert 6.02 \times 10^1 km to centimeters by multiplying by 100,000 cm/km.

Calculate the value of 6.02 \times 10^1 km in centimeters.

Compare the two values: 5.63 \times 10^6 cm and the converted value of 6.02 \times 10^1 km in cm to determine which is larger.

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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 represented as a product of a number between 1 and 10 and a power of ten. For example, 5.63 * 10^6 means 5.63 multiplied by 1,000,000. Understanding this notation is essential for comparing large quantities.

Unit Conversion

Unit conversion involves changing a quantity expressed in one unit to another unit. In this question, we need to convert kilometers to centimeters to make a direct comparison. Since 1 kilometer equals 100,000 centimeters, converting 6.02 * 10^1 km to centimeters is crucial for determining which quantity is larger.

Magnitude Comparison

Magnitude comparison refers to the process of determining which of two quantities is larger. This involves evaluating the numerical values and their respective units after any necessary conversions. By comparing the magnitudes of the two quantities in the same unit, we can accurately identify which one is larger.

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