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Chapter 1: Problem 15

Express each value in exponential form. Where appropriate, include units in your answer. (a) speed of sound (sea level): 34,000 centimeters per second (b) equatorial radius of Earth: 6378 kilometers (c) the distance between the two hydrogen atoms in the hydrogen molecule: 74 trillionths of a meter (d) $\frac{\left(2.2 \times 10^{3}\right)+\left(4.7 \times 10^{2}\right)}{5.8 \times 10^{-3}}=$

Short Answer

Expert verified
(a) \(3.4 \times 10^{4}\) cm/sec, (b) \(6.378 \times 10^{3}\) km, (c) \(7.4 \times 10^{-11}\) m, (d) \(4.6 \times 10^{5}\).

Step by step solution

01

Express the Speed of Sound in Exponential Form

To express the speed of sound in exponential form, identify the power of ten that the number 34,000 can be represented by. It can be seen that 34,000 = 3.4 x 10^4. Hence, the speed of sound at sea level is \(3.4 \times 10^{4}\) centimeters per second.
02

Express the Equatorial Radius of Earth in Exponential Form

To express 6378 kilometers in exponential form, observe that 6378 = 6.378 x 10^3. Hence, the equatorial radius of Earth is \(6.378 \times 10^{3}\) kilometers.
03

Express the Distance between Hydrogen Atoms in Exponential Form

To express 74 trillionths of a meter in exponential form, note that a trillionth is equivalent to \(10^{-12}\). Therefore, 74 trillionths = 74 x \(10^{-12}\), which simplifies to \(7.4 \times 10^{-11}\). Hence, the distance between the hydrogen atoms in a hydrogen molecule is \(7.4 \times 10^{-11}\) meters.
04

Evaluate the Given Expression

Observe that the result of the expression will depend on the rules of operations, i.e., the order of operations: parentheses first, then multiplication and division (from left to right). \n To simplify the expression, begin by solving the operation in the parenthesis: \(2.2 \times 10^{3} + 4.7 \times 10^{2} = 2.2 \times 1000 + 4.7 \times 100 = 2200 + 470 = 2670\). \n Then divide this result by \(5.8 \times 10^{-3}\): \(\frac{2670}{5.8 \times 10^{-3}}\), which simplifies to \(4.6 \times 10^{5}\).

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