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Chapter 5: Problem 3

Perform the indicated operation. $$-8.003-2.2$$

Short Answer

Expert verified
-10.203

Step by step solution

01

- Identify the Numbers

Identify the numbers involved in the operation. In this case, the two numbers are -8.003 and -2.2.
02

- Align Decimal Points

Align the decimal points of the two numbers to ensure accurate subtraction. -8.003 -2.200
03

- Perform the Subtraction

Subtract the second number from the first number, paying attention to the negative signs. You will essentially add the absolute values of the two negative numbers: -8.003 - 2.200 = - (8.003 + 2.2) = -10.203

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Key Concepts

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

Decimal Subtraction
When subtracting decimal numbers, it鈥檚 important to align the decimal points. This ensures each digit is in the correct place value. For example, if you are subtracting -8.003 with -2.2, align them like this:

- 8.003
- 2.200

Notice that we added an extra zero to -2.2 to make the decimal places equal. This makes subtraction easier and more accurate. Always ensure you maintain the correct number of decimal places.
Negative Numbers
Dealing with negative numbers can be tricky. When you see a subtraction problem involving negative numbers, remember that subtracting a negative is the same as adding a positive. However, in this exercise, you are subtracting a negative from another negative: $$ -8.003 - 2.2.$$

To simplify, think of it as: $$- (8.003 + 2.2) = -10.203.$$

Here, you added the absolute values (ignoring the negative signs initially) and then placed the negative sign back on the result.
Absolute Value
The absolute value of a number is its distance from zero on a number line, regardless of direction. For instance, the absolute value of -8.003 is 8.003, and the absolute value of -2.2 is 2.2.

When performing operations with negative numbers, it's often helpful to consider their absolute values first. In our problem, we first find the absolute values: $$ | -8.003 | = 8.003 $$ $$ | -2.2 | = 2.2.$$

Then, add them: $$ 8.003 + 2.2 = 10.203.$$

Finally, since both numbers were negative, the result of the original problem is also negative.
Basic Arithmetic
Understanding basic arithmetic operations is crucial for solving any math problem, including those involving decimals and negative numbers. Arithmetic operations include addition, subtraction, multiplication, and division.

When subtracting two negative numbers like in $$ -8.003 - 2.2 $$ the process involves adding the absolute values and making the result negative. In this example, you perform the following steps:
  • Find the absolute values: 8.003 and 2.2.
  • Add them: 8.003 + 2.2 = 10.203.
  • Apply the negative sign to the result: -10.203.
Breaking down the problem into these basic steps makes it easier to manage and understand.

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Most popular questions from this chapter

Certain DVD titles are on sale for 2 for \(\$ 32\). If they regularly sell for \(\$ 19.99,\) how much can a person save by buying 4 DVDs?

A bicycle wheel has a 26 -in. diameter. a. Find the circumference. Use 3.14 for \(\pi\) b. How many times will the wheel have to turn to go a distance of 1000 ft \((12,000 \text { in.) } ?\) Round to the nearest whole unit.

For Exercises \(71-82,\) simplify by using the order of operations. $$2.2-\left[9.34+(1.2)^{2}\right]$$

For Exercises \(59-66,\) simplify the expressions. $$(0.4)^{2}$$

Perform the indicated operations. Round the answer to the nearest hundredth when necessary. $$(2.3)\left(\frac{5}{9}\right)$$
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