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Chapter 0: Problem 141

The mad Dr. Frankenstein has gathered enough bits and pieces (so to speak) for \(2^{-1}+2^{-2}\) of his creature-to-be. Write a fraction that represents the amount of his creature that must still be obtained.

Short Answer

Expert verified
Dr. Frankenstein must still obtain \(\frac{1}{4}\) of his creature.

Step by step solution

01

Compute \(2^{-1}\)

The number \(2^{-1}\) is equivalent to the fraction \(\frac{1}{2}\). When the negative power is used, it simply means we take the reciprocal of the base.
02

Compute \(2^{-2}\)

Similarly, \(2^{-2}\) translates to \(\frac{1}{2^2}\) which is \(\frac{1}{4}\). Thus, \(2^{-2}\) is equivalent to \(\frac{1}{4}\).
03

Add the Computed Fractions

Add the fractions \(\frac{1}{2}\) and \(\frac{1}{4}\). The result is \(\frac{3}{4}\). This is the total portion of the creature that Dr. Frankenstein currently has.
04

Calculate the Remaining Fraction

Since Dr. Frankenstein wants to complete 1 whole creature, subtract the portion he already has from 1. So \(1 - \frac{3}{4}\) results in \(\frac{1}{4}\). This is the fraction that he still needs to gather to complete his creature.

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Most popular questions from this chapter

The formula for converting Celsius temperature, \(C,\) to Fahrenheit temperature, \(F\), is $$F=\frac{9}{5} C+32$$ If Fahrenheit temperature ranges from \(41^{\circ}\) to \(50^{\circ},\) inclusive, what is the range for Celsius temperature? Use interval notation to express this range.

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{1}{2}+\frac{2}{3}$$

What is a quadratic equation?

Explain how to factor \(3 x^{2}+10 x+8\).

$$\text { Solve for } t: s=-16 t^{2}+v_{0} t$$
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