Problem 40 - Introductory and Intermediate Algebra for College Students 4th

Question

Perform the indicated subtraction. $$5.7-3.3$$

Step-by-Step Solution

Answer

The result of the subtraction is 2.4

Step 1: Align the Numbers

First, align decimal places of both numbers, as following: \[5.7 \ -3.3 \] The dot under each number should be vertically aligned.

Step 2: Perform the Subtraction

Subtract each pair of digits. Be sure to subtract each digit in its correct place starting from the smallest place value which is the tenths place in this case. \(5.7 - 3.3 = 2.4\)

Key Concepts

Aligning Decimal Places

Understanding the alignment of decimal places is crucial for accurately performing operations like subtraction. This approach ensures that digits with the same place value are aligned correctly before the calculation is performed. For instance, subtracting 5.7 and 3.3 requires you to write one number directly above the other with the decimal points lined up:

5.7
-3.3
_____
With both numbers aligned, this setup ensures that each digit is directly above or below its counterpart from the other number. Each digit’s position in relation to the decimal point indicates its value: for numbers to the left of the decimal point, each digit represents whole numbers and those to the right represent portions of a whole.

Subtraction of Decimals

Subtraction of decimals is analogous to the subtraction of whole numbers, with the additional step of aligning the decimal points. When performing the operation, start from the rightmost digits, which have the lowest place value (usually the tenths), and work to the left, just like in the given example:
5.7
-3.3
_____
2.4

Here, 7 tenths minus 3 tenths equals 4 tenths, and 5 minus 3 equals 2. As there are no whole numbers to carry or borrow from in this example, the subtraction is straightforward. However, when a lower place value is larger than its counterpart, you would need to 'borrow' from the next highest place value - an operation students often perform in whole number subtraction.

Place Value

Place value is a fundamental concept of decimals, as it determines the value of the digit depending on its location. In the given exercise, the number 5.7 consists of the digit 5 in the ones place and 7 in the tenths place. Similarly, 3.3 has 3 in the ones place and 3 in the tenths place. The ones place represents whole units, and as you move to the right of the decimal point, each place value represents ten times smaller than the one before it (tenths, hundredths, thousandths, etc.).

Understanding place value is important not only in subtraction but in all arithmetic operations. It helps maintain consistency in the calculation and avoids common mistakes that can occur due to misaligned digits or incorrect positioning of the decimal point during calculations.