Select the correct answer.
Which value is equivalent to 178 centimeters?
A. 1.78 millimeters
B. 17.8 millimeters
C. 1.78 meters
D. $1.78 \times 10^{-2}$ micrometers
E. $1.78 \times 10^{-5}$ kilometers
Answer (2)
Convert 178 cm to millimeters: 178 × 10 = 1780 mm.
Convert 178 cm to meters: 100 178 = 1.78 m.
Convert 178 cm to micrometers: 178 × 1 0 4 = 1.78 × 1 0 6 μm.
Convert 178 cm to kilometers: 1 0 5 178 = 1.78 × 1 0 − 3 km.
The correct answer is 1.78 meters: C .
Explanation
Problem Analysis We are given a length of 178 centimeters and need to find the equivalent value from the given options. We will convert 178 centimeters to millimeters, meters, micrometers, and kilometers to compare with the options.
Convert to Millimeters To convert centimeters to millimeters, we use the conversion factor 1 cm = 10 mm. Therefore, 178 cm = 178 * 10 mm = 1780 mm. Option A is 1.78 mm and option B is 17.8 mm, so neither of these are correct.
Convert to Meters To convert centimeters to meters, we use the conversion factor 1 m = 100 cm. Therefore, 178 cm = 178 / 100 m = 1.78 m. Option C is 1.78 meters, which matches our calculation.
Convert to Micrometers To convert centimeters to micrometers, we use the conversion factor 1 cm = 1 0 4 micrometers. Therefore, 178 cm = 178 * 1 0 4 micrometers = 1.78 × 1 0 6 micrometers. Option D is 1.78 × 1 0 − 2 micrometers, which is not correct.
Convert to Kilometers To convert centimeters to kilometers, we use the conversion factor 1 km = 1 0 5 cm. Therefore, 178 cm = 178 / 1 0 5 km = 1.78 × 1 0 − 3 km. Option E is 1.78 × 1 0 − 5 kilometers, which is not correct.
Final Answer Comparing the converted values with the given options, we find that 178 centimeters is equivalent to 1.78 meters. Therefore, the correct answer is C.
Examples
Imagine you're building a model airplane and the instructions are in centimeters, but your ruler is in meters. Converting between these units is essential to ensure your model is the correct size. Similarly, if you're working with very small components measured in micrometers, knowing how to convert to more common units like centimeters helps in ordering the right parts. Understanding unit conversions is crucial in many practical applications, from construction to engineering.
The equivalent value to 178 centimeters is 1.78 meters, which matches option C. All other options do not represent the correct conversion. Thus, the answer is C.
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