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Chapter 8: Problem 43

Perform each indicated operation on decimals. $$ (0.236)(-100) $$

Short Answer

Expert verified
The product is \(-23.6\).

Step by step solution

01

Understand the Problem

We need to multiply the decimal number \(0.236\) by \(-100\). This involves understanding how to handle the multiplication of decimals and negative numbers.
02

Multiply the Numbers Ignoring the Sign

First, ignore the negative sign and multiply \(0.236\) by \(100\). This is done by moving the decimal point two places to the right, turning \(0.236\) into \(23.6\).
03

Apply the Negative Sign

After computing the multiplication ignoring the negative sign, apply the negative sign back to the result. So, \(23.6\) becomes \(-23.6\).

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Key Concepts

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

Multiplication with Negative Numbers
When you encounter multiplication problems involving a negative number, it might seem a bit tricky, but it's really quite simple. There is a straightforward rule to remember. When you multiply a positive number by a negative number, the product is always negative.
To clearly grasp this concept, consider:
  • Positive 脳 Positive = Positive
  • Negative 脳 Negative = Positive
  • Positive 脳 Negative = Negative
In our original exercise, we are multiplying a decimal, 0.236, by a negative whole number, -100. So, the outcome will be negative as positive 0.236 is multiplied by negative 100. We apply this in the last stage of our solution.
Understanding Decimals
Decimals are numbers that contain a decimal point, which separates the whole part of the number from the fractional part. They can represent amounts less than one, exactly one, or greater than one.
Understanding how to multiply decimals involves:
  • Recognizing what the decimal point means in terms of shifting positions鈥攊n other words, what happens to the decimal point when numbers are increased or decreased by factors of 10.
  • Knowing how to perform operations with decimals by treating them like whole numbers during calculations, then adjusting the decimal accordingly.
In multiplication, such as in the exercise with 0.236 and -100, moving the decimal point helps simplify calculations:
  • We multiply 0.236 by 100, moving the decimal point two places right, turning 0.236 into 23.6.
  • Finally, we adjust for any negative or positive signs involved.
Step by Step Solution
Following a systematic approach is essential in solving any mathematical problem. In the exercise, resolving decimal multiplication while considering the negative sign involves understanding and following steps, keeping the process clear.
Here's the breakdown:
  • Step 1: Recognize that you are performing multiplication involving a decimal number by a negative integer鈥攈ere, 0.236 and -100.
  • Step 2: Multiply like it鈥檚 all positive; ignore the negative sign initially. Multiply 0.236 by 100. This means shifting the decimal two positions to the right, so 0.236 becomes 23.6.

  • Step 3: After calculating the product using the positive values, reintroduce the negative sign to the final result because we initially ignored it. Thus, 23.6 becomes -23.6.
These steps will consistently help solve similar problems where multiplication involves decimals and negative numbers.

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