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Chapter 5: Problem 689

In the following exercises, simplify each expression. $$ 15.4+3.02 $$

Short Answer

Expert verified
18.42

Step by step solution

01

Align the Decimal Points

Write down the numbers vertically, aligning the decimal points to make addition easier: \( \begin{array}{r} 15.4 \ 3.02 \ \end{array} \)
02

Add Each Column

Starting from the right and moving to the left, add each column just like in regular addition. Ensure to carry over any extra value to the next column if necessary: \( \begin{array}{r} 15.40 \ +3.02 \ \hline 18.42 \end{array} \)

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Key Concepts

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

Aligning Decimal Points
When performing decimal addition, the first key step is aligning the decimal points. This ensures that the digits in each column represent the same place value.
By aligning the numbers based on their decimal points, you're making sure that each column contains similar values such as units, tenths, and hundredths.
For instance, in the exercise, you write 15.4 and 3.02 directly under each other, aligning the decimal points as follows:
15.4
3.02
This arrangement simplifies the addition process and helps avoid errors. You may also add an extra zero to the 15.4, making it 15.40, to match the number of decimal places in 3.02.
Step-by-Step Addition
Once the decimal points are aligned, you can start the step-by-step addition. Begin adding from the rightmost column and move leftwards, similar to how you add whole numbers.
Let's break it down:
  • In the hundredths place, you have 0 and 2, which sum up to 2.
  • In the tenths place, you add 4 and 0, resulting in 4.
  • In the units place, you add 5 and 3, which equals 8.
So far, your result looks like this: 18.42.
Remember to add each digit from right to left to ensure no values are missed. Also, watch for extra zeros; these will guide you through the process.
Carrying Over in Addition
Carrying over is an essential step in addition, especially when the sum in any column exceeds 9. Though it wasn't necessary in this exercise, let's understand the concept.
Assume you're adding 15.49 and 3.62.
In the hundredths place, you get 9+2 which equals 11. Write down 1 and carry over 1 to the tenths place.
Now, add the tenths place: 4+6 (plus the 1 carried over), resulting in 11. Again, write down 1 and carry over 1 to the units place.
Sum up the units place: 5+3 (plus the 1 carried over), resulting in 9.
Your final result will be 19.11.
Carrying over ensures that each column remains accurate and balanced, maintaining the integrity of the addition process.

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