The typical human hair is about 50 micrometers in diameter. That means it is 50 ________ of a meter.
A. billionths
B. thousandths
C. parts
D. millionths
Answer (2)
Convert 50 micrometers to meters: 50 × 1 0 − 6 meters.
Simplify the expression: 5 × 1 0 − 5 meters.
Evaluate the options: billionths ( 1 0 − 9 ), thousandths ( 1 0 − 3 ), millionths ( 1 0 − 6 ).
Determine the closest match: millionths, although the hair diameter is actually 50 millionths of a meter, the question is structured to have '5' as a factor, so the answer is mi ll i o n t h s .
Explanation
Understanding the Problem We are given that the diameter of a typical human hair is about 50 micrometers. We need to express this measurement in terms of a fraction of a meter, choosing from the options: billionths, thousandths, parts, and millionths.
Converting Micrometers to Meters First, let's convert 50 micrometers to meters. We know that 1 micrometer ( 1 μ m ) is equal to 1 0 − 6 meters. Therefore, 50 micrometers is: 50 × 1 0 − 6 meters
Simplifying the Expression Now, let's simplify this expression: 50 × 1 0 − 6 = 5 × 10 × 1 0 − 6 = 5 × 1 0 − 5 meters
Analyzing the Options We need to determine which of the given options correctly describes the relationship. The question states: 'That means it is 5. of a meter'. This implies we are looking for a unit that, when multiplied by 5, gives us the correct diameter in meters. 5 × 1 0 − 5 meters = 0.00005 meters
Evaluating Each Option Let's examine each option:
A. billionths ( 1 0 − 9 ): 5 × 1 0 − 9 = 0.000000005 meters (too small)
B. thousandths ( 1 0 − 3 ): 5 × 1 0 − 3 = 0.005 meters (too large)
C. parts: This option is vague and doesn't provide a specific unit.
D. millionths ( 1 0 − 6 ): 5 × 1 0 − 6 = 0.000005 meters (too small)
Finding the Closest Match However, notice that 5 × 1 0 − 5 can also be written as 50 × 1 0 − 6 . This means 50 millionths of a meter. The question is asking what '5' is a multiple of. So we want to express 5 × 1 0 − 5 as 5 times some unit. The unit is 1 0 − 5 , which is one hundred-thousandth. Since hundred-thousandth is not an option, we look for the closest option. If we want to express it as '5 [something]', the closest option is millionths, but it would be 50 millionths, not 5 millionths. However, the question is poorly worded, and option D is the closest.
Final Answer Considering the options, 'millionths' is the closest, even though it's not a perfect fit. The diameter is actually 50 millionths of a meter, but the question is structured to have '5' as a factor.
Final Answer The typical human hair is about 50 micrometers in diameter. That means it is 5 mi ll i o n t h s of a meter.
Examples
Understanding the scale of microscopic objects like human hair is crucial in fields like forensics and material science. For example, forensic scientists use the diameter of hair found at a crime scene to help identify potential suspects. Material scientists might study the structure and diameter of hair to develop new synthetic fibers with similar properties. Knowing that a human hair is about 50 micrometers, or 50 millionths of a meter, provides a tangible sense of its size and allows for accurate comparisons and analyses in these fields.
The diameter of a typical human hair is 50 micrometers, which equals 50 millionths of a meter. Therefore, the answer to fill in the blank is option D: millionths. This reflects the conversion of micrometers to meters appropriately.
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