Problem 55 - Prealgebra

Question

Perform the indicated operations. $$3+0.25$$

Step-by-Step Solution

Answer

3 + 0.25 = 3.25

Step 1: Understanding the Problem

The exercise asks us to perform the operation of adding the numbers 3 and 0.25 together. It is a simple addition of a whole number and a decimal number.

Step 2: Aligning Decimal Places

To perform this addition, we'll align the numbers by their decimal points. We can write 3 as 3.00 to ensure the placeholder for hundredths is visible. This gives us:\[\begin{aligned}&3.00 \ +&0.25 \\hline&\end{aligned}\]

Step 3: Performing the Addition

Starting from the rightmost digit (hundredths place), add 0 + 5 = 5. Move to the tenths place, add 0 + 2 = 2. Finally, in the units place, add 3 + 0 = 3. The sum is:\[\begin{aligned}&3.00 \ +&0.25 \\hline&3.25\end{aligned}\]

Step 4: Concluding the Solution

The addition of 3 and 0.25 results in a sum of 3.25. Make sure to express the answer with the correct number of decimal places.

Key Concepts

Understanding Place Value

Place value is a crucial concept in learning about numbers, especially when dealing with both whole numbers and decimals. Each digit in a number has a specific place value, which determines its worth within the whole number or decimal.

• In whole numbers, place value increases by powers of 10 from right to left. For example, in the number 3, the 3 is in the units place, representing 3 ones or simply 3.
• When dealing with decimals, the place value of digits decreases by powers of 10 from left to right. For instance, in 0.25, the 2 is in the tenths place, and the 5 is in the hundredths place.

Understanding place value is essential as it helps accurately align numbers when performing arithmetical operations like addition and subtraction, ensuring each digit is in the correct column for calculation.

What Are Whole Numbers?

Whole numbers are the set of numbers that include all non-negative integers from zero upwards. They do not have decimal or fractional parts, making them distinct from decimal numbers.

• The series of whole numbers is infinite, starting from 0, 1, 2, 3, and so on.
• Whole numbers are often used in situations involving counting or ordering.

In the context of our exercise, the number 3 is a whole number. When we perform operations like addition involving whole numbers and decimals, it is important to recognize the nature of each number. This is because their representation is different, for instance, 3 can be written as 3.00 to align with a decimal format.

Basic Arithmetical Operations

Arithmetical operations are foundational mathematical operations that include addition, subtraction, multiplication, and division. These operations allow us to manipulate numbers and solve various mathematical problems.

• Addition: This operation brings two or more numbers together to find their total or sum. When adding decimals, it is important to align the numbers by their decimal points.
• Subtraction: This operation finds the difference between numbers, subtracting one from another.
• Multiplication: This operation calculates the total of one number repeated a certain number of times.
• Division: This operation splits a number into equal parts.

In the exercise, our main focus is on addition, specifically adding a whole number to a decimal. Properly aligning decimal places ensures an accurate sum, making correct use of place value. By adding 3 (represented as 3.00) and 0.25 vertically, we accurately compute the sum of 3.25.