Question

Perform the indicated operations. Give exact answers. \(20.3+8.57+0.03=\) ______

Short answer

The exact answer is 28.90.

Step-by-step solution

Align the Numbers

Write down the numbers 20.3, 8.57, and 0.03 vertically aligning them by their decimal points. This alignment helps you correctly add the decimal places.

Adjust the Decimal Places

To ensure we can add these numbers easily, make sure each number has the same number of decimal places. Convert 20.3 to 20.30 (two decimal places) and confirm that all numbers now have two decimal places: 20.30, 8.57, and 0.03.

Add the Numbers

Start adding from the rightmost decimal place moving to the left. Add the hundredths: 0 + 7 + 3 = 10, write down 0 and carry over 1. Next, add the tenths: 3 + 5 + 0 + 1 (carry) = 9. Now add the whole numbers: 20 + 8 = 28. Thus, the sum is 28.90.

Key concepts

Decimal Addition

Adding decimals can seem tricky at first, but don't worry, it's actually straightforward. The process of decimal addition involves adding numbers that have a decimal point, and it requires careful attention to detail. When you are adding decimals, you want to make sure every part of the numbers line up correctly, especially their decimal points. This ensures you're directly adding the same place values together, like tenths to tenths and hundredths to hundredths. The sum of all these will yield the final result. Nevertheless, to get to the right result, there are a few steps to follow.

Place Value Alignment

Place value alignment is a crucial part of working with decimals in addition. Without aligning your numbers properly, you may mix up different place values and end up with the wrong answer. To prevent this, you need to vertically align the numbers by their decimal points. This ensures that digits of the same place value line up properly. For instance:

• Align the decimal numbers so that the decimal points are one beneath the other.
• Pad with zeros where necessary to make each number have the same number of decimal places.

This gives you a clearer view, allowing for more accurate addition. For example, aligning 20.3, 8.57, and 0.03 properly follows: - Convert 20.3 to 20.30. - Ensure every number has two decimal places. Once aligned, you can proceed to add each digit in columns, from rightmost to left, ensuring easier handling of any required carry-overs.

Carrying Over in Addition

Carrying over in addition is something you might remember from adding whole numbers, and the concept remains the same with decimals! When adding digits in a particular column exceeds 9, you need to carry over the additional value to the next left column. Consider this example:

• Add the digits in the hundredths place: 0 + 7 + 3 = 10. Write down 0 and carry over the 1.
• Add the tenths place: 3 + 5 + 0 + 1 (from the carry over) = 9.
• Add the whole number place: 20 + 8 = 28.

Carrying over is an essential step to ensure that your additions remain accurate, especially when dealing with columns that add up to ten or more. By systematically carrying over values, you maintain the integrity of each place value, leading you to a correct final answer like 28.90 in this exercise.