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Chapter 15: Problem 6

Write each of the following in an acceptable form without using a decimal point: a) \(0.0000546 \mathrm{~kW} / \mathrm{K}\) b) \(65.3207 \mathrm{kH} / \mathrm{kg}\) c) \(54.6367 \times 10^{-6} \mathrm{MF} / \mathrm{kg}\)

Short Answer

Expert verified
a) 0.0000546 kW/K b) 65.3207 kH/kg c) 54.6367 x 10^{-6} MF/kg a) The equivalent expression for 0.0000546 kW/K is \(5.46 \times 10^{-5} \mathrm{~kW} / \mathrm{K}\). b) The equivalent expression for 65.3207 kH/kg is \(6.53207 \times 10^{2} \mathrm{~kH} / \mathrm{kg}\). c) The equivalent expression for 54.6367 x 10^{-6} MF/kg is \(5.46367 \times 10^{-5} \mathrm{~MF} / \mathrm{kg}\).

Step by step solution

01

a) 0.0000546 kW/K conversion

First, let's convert the decimal number to scientific notation. To do this, we need to move the decimal point five places to the right, making the new number 5.46. The power of ten is obtained by counting the number of places moved; in this case, it is -5. Thus, we have \(5.46 \times 10^{-5} \mathrm{~kW} / \mathrm{K}\) as the equivalent expression.+
02

b) 65.3207 kH/kg conversion

Now, let's convert the decimal number to scientific notation. Move the decimal point two places to the left to get the new number 6.53207. Counting the number of places moved gives us the power of ten, which is +2 in this case. So, the equivalent expression will be \(6.53207 \times 10^{2} \mathrm{~kH} / \mathrm{kg}\).
03

c) 54.6367 x 10^{-6} MF/kg conversion

In this expression, we already have a power of ten, but we still need to convert the decimal number to scientific notation. Move the decimal point one place to the left to get the new number 5.46367 and add the power of ten moved to the existing power. In this case, we moved the decimal point by 1, and the original power was -6. Thus, the new power will be -6 + 1 = -5. The equivalent expression will be \(5.46367 \times 10^{-5} \mathrm{~MF} / \mathrm{kg}\).

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