Problem 91 - Prealgebra

Question

The problems below review some of the material on solving equations. Reviewing these problems will help you with the next section. Solve. $$(1.2)^{2}$$

Step-by-Step Solution

Answer

1.44

Step 1: Recognize the Expression

We need to solve the expression \((1.2)^2\). This is an example of a power notation, where we need to square the number 1.2.

Step 2: Understand Squaring a Number

Squaring a number means multiplying the number by itself. Therefore, \( (1.2)^2 = 1.2 \times 1.2 \).

Step 3: Perform the Multiplication

Perform the multiplication: \(1.2 \times 1.2\). To multiply, first convert the decimals to fractions or perform the multiplication directly. For direct multiplication, \(1.2 \times 1.2 = 1.44\).

Step 4: Confirm the Result

Double-check the multiplication to confirm the result is accurate: \(1.2 \times 1.2 = 1.44\). If calculated correctly, these numbers will confirm the result.

Key Concepts

Squaring Numbers

Squaring a number is a fundamental mathematical operation that you often encounter. It means taking a number and multiplying it by itself. Consider the example of squaring the number 1.2. When you square 1.2, you're essentially performing the operation:

• Multiply 1.2 by 1.2, which will give the result as part of the process.
• This results in 1.44, because 1.2 times 1.2 equals 1.44.

Squaring numbers have implications in different contexts, such as finding the area of a square. When you're determining the space within a square, if one side is represented by the number 1.2, its area is given by squaring 1.2, which is \[ 1.2 \times 1.2 = 1.44 \].
This concept is widely used in algebra and geometry. Remember, a square operation will always result in a positive number since multiplying two positives or two negatives results in a positive output.

Power Notation

Power notation is a way to express repeated multiplication of a number by itself. When you see a number like \(1.2^2\), this is power notation meaning 1.2 raised to the power of 2. In simpler terms:

• The base is 1.2, indicating the number that gets multiplied.
• The exponent, in this case, is 2, telling us how many times to multiply the base.

Hence, \(1.2^2\) is calculated by multiplying 1.2 by itself, as shown in the expression \(1.2 \times 1.2\). Understanding power notation is crucial as it is frequently used in higher-level mathematics to simplify numbers and expressions. For instance, \(10^3\) means \(10 \times 10 \times 10\), which equals 1000.
Power notation provides a compact way to express large or repetitive calculations efficiently. This becomes incredibly useful in algebra and scientific calculations where numbers can become very large or very small.

Multiplying Decimals

1.2 times 1.2 is an example of multiplying decimals. When you work with decimals, it's all about precise placement of the decimal point. Here are some steps you might find helpful:

• Start by ignoring the decimal points and multiply the numbers as if they were whole numbers. For 1.2 multiplied by 1.2, you multiply 12 by 12.
• Now, calculate \(12 \times 12 = 144\).
• After multiplying, count the total number of decimal places in the numbers you multiplied. Each decimal in the number contributes one position. Since there is one decimal place in 1.2 and another in the second 1.2, that's two decimal places total.
• You then place the decimal point in your result 144 by moving two places from the right: thus, 144 becomes 1.44.

Multiplying decimals might seem tricky, but with practice, it becomes straightforward. Always remember, after basic multiplication, to return to your decimal and place it in the right position. This makes sure your results maintain accuracy.