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

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.