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Chapter 1: Problem 23

Convert these to nonscientific notation: (a) \(1.52 \times\) \(10^{4},\) (b) \(7.78 \times 10^{-8}\)

Short Answer

Expert verified
(a) \(1.52 \times 10^{4}\) in nonscientific notation is 15200, and (b) \(7.78 \times 10^{-8}\) in nonscientific notation is 0.0000000778.

Step by step solution

01

Conversion of (a)

The number \(1.52 \times 10^{4}\) has a positive exponent, indicating that it is greater than 1. Convert this by moving the decimal point to the right according to the value of the exponent, which is 4 in this case. That results in \(15,200\).
02

Conversion of (b)

The number \(7.78 \times 10^{-8}\) has a negative exponent, indicating that it is a fraction, less than 1. Convert this by moving the decimal point to the left according to the value of the exponent, which is 8 in this case. This results in \(0.0000000778\). Remember to pad with zeros accordingly.

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Most popular questions from this chapter

Suppose that a new temperature scale has been devised on which the melting point of ethanol \(\left(-117.3^{\circ} \mathrm{C}\right)\) and the boiling point of ethanol \(\left(78.3^{\circ} \mathrm{C}\right)\) are taken as \(0^{\circ} \mathrm{S}\) and \(100^{\circ} \mathrm{S}\), respectively, where \(\mathrm{S}\) is the symbol for the new temperature scale. Derive an equation relating a reading on this scale to a reading on the Celsius scale. What would this thermometer read at \(25^{\circ} \mathrm{C} ?\)

The medicinal thermometer commonly used in homes can be read to \(\pm 0.1^{\circ} \mathrm{F}\), whereas those in the doctor's office may be accurate to \(\pm 0.1^{\circ} \mathrm{C}\). In degrees Celsius, express the percent error expected from each of these thermometers in measuring a person's body temperature of \(38.9^{\circ} \mathrm{C}\).

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Express these numbers in scientific notation: (a) 0.000000027 , (b) 356 (c) 0.096 .
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