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Chapter 1: Problem 16

Evaluate. $$ (1.5)^{2} $$

Short Answer

Expert verified
The value of \((1.5)^2\) is 2.25.

Step by step solution

01

Understand the Problem

We need to evaluate the expression \((1.5)^2\). This means we must calculate the square of 1.5, which is multiplying 1.5 by itself.
02

Rewrite as a Multiplication

Rewrite the expression \((1.5)^2\) as a multiplication problem: \(1.5 \times 1.5\).
03

Multiply the Numbers

Multiply 1.5 by 1.5. First, ignore the decimal place and multiply 15 by 15, which equals 225. Since there are two decimal places in the factors, put the decimal point so that the product has two decimal places: 2.25.

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Key Concepts

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

Squaring Numbers
The concept of squaring involves taking a number and multiplying it by itself. It's often denoted with a small '2' written just above and to the right of a number, like this:
  • Squaring grows numbers quickly, especially as they become larger.
  • Think of squaring as just another way to say "multiplying it by itself."
So, when the problem asks you to find \((1.5)^2\), it's requesting you to calculate \(1.5 \times 1.5\). Squaring is a foundational skill in mathematics, used often in geometry, algebra, and even in real-life applications like calculating areas of square plots.
Multiplication
Multiplication is a key arithmetic operation involving the product of two numbers. In our case with the exercise, the multiplication is done like this:
  • Ignore decimal places to simplify calculation initially.
  • For \(1.5 \times 1.5\), consider it as \(15 \times 15\), which equals \(225\).
  • Don't forget to adjust for decimals at the end!
Place the decimal in the product by counting the digits to the right of the decimal point in both numbers. Here, each has one digit, so the product will have two: \(2.25\). Multiplication is straightforward but remembering to adjust for decimals ensures accuracy.
Decimal Numbers
Decimal numbers are numbers that have a point or dot separating the whole number from the fractional part. They are used to represent values that aren't whole and are crucial across various mathematical applications. Here's why understanding decimals matters:
  • Decimals allow us to express fractions in a simple, readable format.
  • When multiplying decimals like \(1.5 \times 1.5\), ignore the decimal points for easy calculation first.
  • Adjust the final answer by making sure all decimal places in the factors are accounted for in the result.
Decimals can seem tricky at first. However, once you grasp placing the decimal correctly, calculations become much more straightforward. In our example, \(225\) becomes \(2.25\) due to the two decimal places present in our factors.

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Solve. The coldest temperature ever recorded in the United States was \(-80^{\circ} \mathrm{F}\) in Alaska. The warmest temperature ever recorded was \(134^{\circ} \mathrm{F}\) in California. How many degrees warmer is \(134^{\circ} \mathrm{F}\) than \(-80^{\circ} \mathrm{F} ?\) (Source: The World Almanac, 2005)
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