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Chapter 5: Problem 81

Perform the indicated operations. $$3.6+0.04$$

Short Answer

Expert verified
The sum is 3.64.

Step by step solution

01

Align the Decimals

First, ensure that the numbers are aligned by their decimal points to facilitate addition. Write \(3.6\) and \(0.04\) so that the decimal points are one above the other: \[\begin{array}{c} 3.60 \+0.04 \\hline\end{array}\]
02

Add the Numbers

Add the numbers column by column from right to left. Starting from the hundredths place: - Hundredths place: \(0 + 4 = 4\)- Tenths place: \(6 + 0 = 6\)- Units place: \(3\) remains unchanged\[\begin{array}{c} 3.60 \+0.04 \\hline 3.64\end{array}\]
03

Write Down the Result

The result of the addition is \(3.64\), which combines the units, tenths, and hundredths places from the calculation above.

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Key Concepts

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

Aligning Decimals
When you add decimals, it's crucial to properly align them first. Misalignment can lead to incorrect results, so take your time with this step! Place the numbers directly underneath each other, ensuring that the decimal points line up vertically. This ensures that each digit aligns with its respective place value, such as tenths with tenths, hundredths with hundredths, and so on.

For example, when adding 3.6 and 0.04, note how these numbers are placed one on top of the other. You should write them as:
  • 3.60
  • + 0.04
By filling in any missing digits with zeros, such as writing 3.6 as 3.60, you maintain the structure and ease of addition for places like hundredths and tenths.
Adding Decimals
Once your decimals are perfectly aligned, the addition process begins. Work from right to left, similar to how you add whole numbers. Start by adding the digits in the smallest place value you have, often the hundredths place.

For our example, adding 3.6 and 0.04:
  • Hundredths: 0 + 4 = 4
  • Tenths: 6 + 0 = 6
  • Units: 3 stays as 3, since 0 in 0.04 doesn't affect it
After adding each column, proceed to the next on the left. If a column's sum exceeds 9, you'll need to carry over to the next column on the left, but in this case, no carrying is needed. The result will be written in the same format, maintaining the decimal point in its original aligned position.
Place Value in Decimals
Understanding place value is pivotal when working with decimals. Place value refers to the position of a digit in a number, dictating the value of the digit itself. For instance, in any decimal number, there are parts representing units, tenths, hundredths, thousandths, and so on as you move rightward from the decimal point.

Take the number 3.64.
  • '3' is in the units place, meaning it's worth 3.
  • '6' is in the tenths place, meaning it's worth 0.6.
  • '4' is in the hundredths place, meaning it's worth 0.04.
Recognizing place value allows for proper operation on each digit during addition and ensures the decimal point is placed accurately in the answer. By aligning, adding, and considering place values effectively, precision in decimal operations is achieved.

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Most popular questions from this chapter

Write each fraction in simplest form. \(\frac{18}{30 y}\)

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