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Chapter 5: Problem 3

Perform the indicated operations. $$(-0.15)^{2}$$

Short Answer

Expert verified
(0.0225)

Step by step solution

01

Understand the operation

The exercise asks to find the square of (-0.15). This means we need to multiply (-0.15) by itself.
02

Apply the exponentiation

Calculate (-0.15)^{2} by multiplying (-0.15) with (-0.15). \((-0.15) \times (-0.15)\)
03

Perform multiplication

When multiplying two negative numbers, the result is positive. \((-0.15) \times (-0.15) = 0.0225\)

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Key Concepts

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

multiplication
Multiplication is a fundamental mathematical operation. It is the process of combining equal groups of objects. Simply put, it involves adding a number to itself a certain number of times. For example, multiplying 3 by 4 (written as \(3 \times 4\)) means adding 3 to itself 4 times: 3 + 3 + 3 + 3 which equals 12.
In the context of our exercise, we multiply (-0.15) by itself to find its square. We write this as \((-0.15) \times (-0.15)\). The multiplication of two numbers involves the following:
  • Multiplying their absolute values
  • Considering the sign of the result based on the multiplication rules
negative numbers
Negative numbers are numbers less than zero. They are often used to represent a deficit or something that is below a baseline. When dealing with negative numbers, certain rules apply for operations like addition, subtraction, and multiplication.
For example, when you multiply two negative numbers, the result is positive. This might seem counterintuitive, but think of it in terms of canceling out. Each negative number negates the negativity of the other, resulting in a positive product. Consider our example, \((-0.15) \times (-0.15)\). Since both numbers are negative, their product, or the 'square' of -0.15, is positive.
square of a number
The square of a number is the result of multiplying that number by itself. It is denoted by raising the number to the power of 2. For instance, \(a^{2}\) means \(a \times a\). Squaring a number always results in a positive value, regardless of whether the original number is positive or negative.
To illustrate, let鈥檚 look at the problem: \((-0.15)^{2}\). This translates to multiplying -0.15 by itself: \((-0.15) \times (-0.15)\). As discussed earlier, the product of two negative numbers is positive, thus the square of -0.15 is 0.0225.
Understanding squaring is crucial as it often appears in various mathematical contexts, including algebra, geometry, and even physics.

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