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Chapter 1: Problem 29

What is the advantage of using scientific notation over decimal notation?

Short Answer

Expert verified
Scientific notation can simplify arithmetic computations and provide an easy way to express and manipulate extremely large or small numbers, unlike decimal notation. It aids in understanding and managing the scale of such numbers.

Step by step solution

01

Understand Decimal Notation

Decimal notation is the regular system we use for expressing numbers. It’s suitable for small and manageable ranges of numbers. But, when we deal with exteremly large or small numbers, decimal notation tends to become cumbersome and it gives no real sense of scale for such numbers.
02

Understanding Scientific Notation

Scientific notation is a mathematical expression used to represent a decimal number between 1 and 10 multiplied by the power of 10. It is usually used when dealing with extremely large or small numbers. For example, the distance between Earth and the nearest galaxy, the Andromeda galaxy, is approximately \(2.537 \times 10^{22}\) meters, it's much easier to comprehend and manage than written in decimal notation.
03

The Advantage

The main advantage of scientific notation is that it can greatly simplify arithmetic computations. In decimal notation, multiplying or dividing long strings of numbers can be complicated and time-consuming. In contrast, with scientific notation, this process could be simplified to multiplying or dividing the significant digits and adding or subtracting the exponents.

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Most popular questions from this chapter

Give an example of a homogeneous mixture and an example of a heterogeneous mixture.

Carry out the following conversions: (a) \(22.6 \mathrm{~m}\) to decimeters, (b) \(25.4 \mathrm{mg}\) to kilograms, (c) \(556 \mathrm{~mL}\) to liters, (d) \(10.6 \mathrm{~kg} / \mathrm{m}^{3}\) to \(\mathrm{g} / \mathrm{cm}^{3}\).

Percent error is often expressed as the absolute value of the difference between the true value and the experimental value, divided by the true value: percent error \(=\frac{\mid \text { true value }-\text { experimental value } \mid}{\mid \text { true value } \mid} \times 100 \%\) The vertical lines indicate absolute value. Calculate the percent error for the following measurements: (a) The density of alcohol (ethanol) is found to be \(0.802 \mathrm{~g} / \mathrm{mL}\). (True value: \(0.798 \mathrm{~g} / \mathrm{mL}\).) (b) The mass of gold in an earring is analyzed to be \(0.837 \mathrm{~g}\). (True value: \(0.864 \mathrm{~g}\).)

One gallon of gasoline in an automobile's engine produces on the average \(9.5 \mathrm{~kg}\) of carbon dioxide, which is a greenhouse gas, that is, it promotes the warming of Earth's atmosphere. Calculate the annual production of carbon dioxide in kilograms if there are 250 million cars in the United States and each car covers a distance of \(5000 \mathrm{mi}\) at a consumption rate of 20 miles per gallon.

The density of methanol, a colorless organic liquid used as solvent, is \(0.7918 \mathrm{~g} / \mathrm{mL}\). Calculate the mass of \(89.9 \mathrm{~mL}\) of the liquid.
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