Alana S.

asked • 10/31/12

How do you find the answer to an equation with a whole number that has a negative power?

The question is 4.0 x 10 to the negative fifth power (-5) The length of the object is about .5 micron. How many could fit to the length of your finger?

Glenda D.

tutor
To solve the problem, we first need to understand what ( 4.0 \times 10^{-5} ) means. The negative exponent indicates that we are dealing with a very small number. Specifically, ( 10^{-5} ) means ( \frac{1}{10^5} ), or ( 0.00001 ). So, we can calculate ( 4.0 \times 10^{-5} ) as follows: [ 4.0 \times 10^{-5} = 4.0 \times 0.00001 = 0.00004 ] This means that the length of the object is ( 0.00004 ) meters, or ( 40 ) microns (since ( 1 ) micron is ( 0.000001 ) meters). Now, to find out how many of these objects could fit along the length of a finger, we need to know the approximate length of a human finger. Let's assume an average finger length is about ( 7 ) centimeters, which is ( 0.07 ) meters. Next, we can calculate how many ( 4.0 \times 10^{-5} ) meter objects fit into ( 0.07 ) meters: [ \text{Number of objects} = \frac{\text{Length of finger}}{\text{Length of object}} = \frac{0.07 \text{ m}}{4.0 \times 10^{-5} \text{ m}} ] Calculating this gives: [ \text{Number of objects} = \frac{0.07}{0.00004} = 1750 ] Therefore, approximately 1750 of these objects could fit along the length of a finger. To solve the problem, we first need to understand what ( 4.0 \times 10^{-5} ) means. The negative exponent indicates that we are dealing with a very small number. Specifically, ( 10^{-5} ) means ( \frac{1}{10^5} ), or ( 0.00001 ). So, we can calculate ( 4.0 \times 10^{-5} ) as follows: [ 4.0 \times 10^{-5} = 4.0 \times 0.00001 = 0.00004 ] This means that the length of the object is ( 0.00004 ) meters, or ( 40 ) microns (since ( 1 ) micron is ( 0.000001 ) meters). Now, to find out how many of these objects could fit along the length of a finger, we need to know the approximate length of a human finger. Let's assume an average finger length is about ( 7 ) centimeters, which is ( 0.07 ) meters. Next, we can calculate how many ( 4.0 \times 10^{-5} ) meter objects fit into ( 0.07 ) meters: [ \text{Number of objects} = \frac{\text{Length of finger}}{\text{Length of object}} = \frac{0.07 \text{ m}}{4.0 \times 10^{-5} \text{ m}} ] Calculating this gives: [ \text{Number of objects} = \frac{0.07}{0.00004} = 1750 ] Therefore, approximately 1750 of these objects could fit along the length of a finger.
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03/25/25

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