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Chapter 4: Problem 12

Add. $$ \begin{array}{r} 13.72 \\ 9.112 \\ 6542.7908 \\ +\quad 23.901 \\ \hline \end{array} $$

Short Answer

Expert verified
6589.5238

Step by step solution

01

Align the Numbers

Write the numbers in a column, aligning the decimal points so that each place value is in line with the others.
02

Pad with Zeros

Add zeroes to the end of the shorter numbers so that each number has the same number of decimal places. The numbers become:13.72009.11206542.790823.9010
03

Add the Numbers

Add the numbers column by column, starting from the rightmost decimal place to the left. Carry over any values as needed.
04

Write the Sum

After adding, the final sum is 6589.5238.

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Key Concepts

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

Aligning Decimals
When adding decimals, it's crucial to line up the decimal points. This ensures that each digit is in its correct place value. Imagine writing a list of numbers but their columns are not aligned; it would be tough to add them correctly. Start by placing the numbers one under the other, making sure the decimal points are directly lined up. This keeps the ones, tens, hundredths, and so on, in their correct columns.
Place Value
Place value refers to the value of each digit in a number based on its position. For example, in the number 6542.7908, the 6 is in the thousands place, the 5 in the hundreds place, the 4 in the tens place, and so on. Understanding place value is essential when dealing with decimal addition. Because each digit must be added to the digit in the same place value column of another number.

By aligning the decimal points, you'll naturally place each digit in its correct column, ensuring accurate addition.
Carrying Over in Addition
Carrying over happens when the sum of numbers in one column is greater than 9. For instance, suppose you are adding 8 + 5 in a column. The sum is 13, so you would write down 3 and carry over 1 to the next column on the left.

This concept is the same in decimal addition. You add digits starting from the rightmost column and move left. When the sum in a column is 10 or more, write down the last digit and add 1 to the next column. This method maintains the integrity of the numerical value across all place values.
Padding with Zeros
Decimal numbers often have different lengths. To simplify addition, add zeros to the end of shorter numbers so that all numbers have the same number of decimal places. This is known as padding with zeros.

For example, aligning and padding the given numbers:
$$ \begin{array}{r} 13.72 \ 9.1120 \ 6542.7908 \ 23.9010 \ \ \ \end{array} $$ makes columns uniform. With uniform columns, it鈥檚 easier to add each place value accurately without missing or misplacing any digit.

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Most popular questions from this chapter

Subtract. $$ 4569-1766 $$

Estimate by rounding as directed. $$ \begin{aligned} &198.67432-24.5007\\\ &\text { nearest ten } \end{aligned} $$

Add. $$ \begin{array}{r} 9.104 \\ +123.456 \\ \hline \end{array} $$

Subtract. $$ \begin{array}{r} 44.345 \\ -\quad 3.105 \\ \hline \end{array} $$

Estimate by rounding as directed. $$ \begin{aligned} &52.367+1.307+7.324 ;\\\ &\text { nearest one } \end{aligned} $$
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