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Chapter 0: Problem 15

In Exercises \(1-28\), compute the numbers. $$ (.01)^{-1} $$

Short Answer

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Step by step solution

01

Identify the given expression

The given expression is \( (.01)^{-1} \). Our goal is to compute the value of this expression.
02

Understand the negative exponent rule

Recall that a negative exponent means taking the reciprocal of the base. For any number \(a^{-1} = \frac{1}{a}\).
03

Apply the negative exponent rule

Given \( (.01)^{-1} \), apply the rule to get \( \frac{1}{.01} \).
04

Convert the decimal to a fraction

Recall that \( .01 = \frac{1}{100} \). So \( \frac{1}{.01} = \frac{1}{\frac{1}{100}} \).
05

Simplify the expression

To simplify \( \frac{1}{\frac{1}{100}} \), multiply by the reciprocal, resulting in \( 100 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

reciprocal
One of the most important concepts in mathematics is the idea of the reciprocal. The reciprocal of a number is simply 1 divided by that number. This is very useful for solving equations and simplifying expressions. For instance, if you have a number like 2, the reciprocal is \(\frac{1}{2}\). Similarly, the reciprocal of 0.5 is \(\frac{1}{0.5} = 2\). Essentially, you flip the number. Reciprocals are particularly important when dealing with negative exponents. A negative exponent tells you to take the reciprocal of the base. For example, \(.01^{-1}\) tells us to take the reciprocal of 0.01, which is \(\frac{1}{0.01}\).
decimal to fraction conversion
Converting decimals to fractions is a crucial skill in math. It helps you simplify expressions and solve equations easily. To convert a decimal to a fraction, you need to understand place values.
For example, in the number 0.01, the 1 is in the hundredths place. So, you can write 0.01 as \( \frac{1}{100} \).
This conversion is essential when dealing with reciprocals and exponents. If you have \(0.01^{-1}\), you first convert 0.01 to the fraction \( \frac{1}{100} \). Next, you find the reciprocal of that fraction, which brings us to \( \frac{100}{1} = 100 \).
simplifying expressions
Simplifying expressions makes math problems easier to solve.
When simplifying, you aim to write expressions in their simplest form. This often involves reducing fractions, combining like terms, or using algebraic rules.
Let's take \( (.01)^{-1} \) as an example. You first apply the negative exponent rule to find the reciprocal: \( \frac{1}{0.01} \).
Then, convert the decimal to a fraction: \( \frac{1}{ \frac{1}{100} } \). Finally, simplify by multiplying by the reciprocal: \( 100 \). Taking these steps ensures that the expression is as simple as possible, making it easy to understand and use in further calculations.

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