Problem 72 - Algebra 1: Concepts and Skills

Question

Find the sum. $$100.02+10$$

Step-by-Step Solution

Answer

The sum of 100.02 and 10 is 110.02

Step 1: Prepare the Numbers for Addition

Position both numbers in a way that the decimal places are aligned accurately. Write them one under the other. It will look like this: 100.02 + 10.00

Step 2: Add the Numbers

Add the numbers column by column from right to left. For the columns without a number, you can assume there is a zero. 100.02 + 10.00 —————- ??.??Start from the extreme right. 2 (from the first number) + 0 (from the second number) = 2. Write this number under the line in the corresponding column. Second column: 0 + 0 = 0. Third column (the one with the decimal points): Again 0 + 0 = 0. Write the decimal point below the line, aligned with the decimal points above. Fourth column: 0 (from the first number) + 1 (from the second number) = 1. Last column: 1 + 0 = 1Write these down, and you will get the final and complete solution of: 110.02

Step 3: Check the Result

For consistency, you may verify the result by using a calculator and performing the same operation to confirm if you got the correct result.

Key Concepts

Decimal Addition

When faced with the task of adding numbers that contain decimal points, such as 100.02 and 10, we engage in decimal addition. This process involves combining the numbers while paying special attention to the correct placement of the decimal point. The importance of aligning the decimal points cannot be underestimated—it is crucial for ensuring accurate results.

A helpful tip for students is always to imagine that there are zeros following the decimal point to fill any gaps. For example, the number 10 can be seen as 10.00 when adding it to another decimal. This step sets a clear path for the addition process as each digit occupies a specific decimal place value, ultimately leading to a precise sum.

Arithmetic Operations

Arithmetic operations form the cornerstone of mathematics, with addition being one of the most fundamental. Whether we're dealing with whole numbers, decimals, or even fractions, the principle remains the same: we aim to compute the total value. With decimals, as seen in the exercise 100.02 + 10, it's not merely about adding numbers—it's about understanding place value and ensuring that each digit is correctly accounted for.

In the broader picture, arithmetic operations with decimals are used in countless real-world applications, such as calculating money, measuring distances, and determining time. Hence, mastering decimal addition is about more than just passing a math class; it's a life skill.

Aligning Decimal Points

The successful addition of decimals begins with one critical step: aligning decimal points. This alignment ensures that each digit is in its correct place value. Think of it as organizing soldiers in a row—the units, tenths, hundredths, and so on, each have their position. When we line up the numbers as in 100.02 and 10.00, we see a clear structure which allows for a direct, column-by-column addition.

An error in alignment can lead to a miscalculation that cascades through the entire problem. Therefore, proper alignment, which may involve adding placeholder zeros, is a skill that significantly impacts the accuracy of decimal arithmetic.

Step-by-Step Addition

Breaking down the process of adding decimals into manageable steps helps students avoid overwhelm and fosters understanding. The method is straightforward: start from the rightmost digits and move left, adding corresponding digits and placing the sum beneath them. By taking the task of decimal addition step by step, as illustrated in the addition of 100.02 with 10.00, learners ensure no place value is overlooked.

Here's a pro tip: always write down the decimal point before adding the other columns, as this anchors the numbers and prevents misalignment. Remember to check your work by recalculating or using tools such as a calculator. This verification step reinforces learning and builds confidence in the process of decimal addition.