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Chapter 5: Problem 152

In the following exercises, divide. $$0.8 \div 0.4$$

Short Answer

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Step by step solution

01

Understand the problem

The problem requires dividing 0.8 by 0.4. The division of decimals can be accomplished by converting them into whole numbers.
02

Convert to whole numbers

To convert the decimals into whole numbers, multiply both the numerator (0.8) and the denominator (0.4) by 10. This changes the division to \[ \frac{8}{4} \].
03

Perform the division

Now, divide 8 by 4. This is a straightforward division: \[ \frac{8}{4} = 2 \].
04

Write the final answer

The result of dividing 0.8 by 0.4 is 2.

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Key Concepts

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

Division of Decimals
Division of decimals might seem tricky at first, but with a clear method, it becomes simple. To divide decimals, we can convert them to whole numbers. This involves multiplying both the numerator and the denominator by the same factor of 10. This adjustment makes the division more straightforward and eliminates the decimal points. The approach remains the same whether you're dealing with tenths, hundredths, or thousandths places. Remember, while you're working with decimals, positioning is crucial, as every digit stands for a specific fraction of ten.
Converting Decimals to Whole Numbers
To simplify decimal division, convert decimals into whole numbers. This process involves multiplying both the numerator and the denominator by the same power of 10. For instance, in our example of dividing 0.8 by 0.4, we multiply both by 10. This changes the problem from \( \frac{0.8}{0.4} \) to \( \frac{8}{4} \). This quits the decimals, making the division easier. This method works because multiplying by 10 (or any other power of 10) shifts the decimal point to the right, converting decimal numbers into whole numbers equivalent without changing their value.
Basic Arithmetic Operations
Understanding basic arithmetic operations such as addition, subtraction, multiplication, and division is vital. In our example, after converting 0.8 and 0.4 to whole numbers, our task changes to dividing 8 by 4. This is a basic division problem recognizable from primary math. Division involves determining how many times one number fits into another. Here, 8 divided by 4 gives us 2. Understanding these arithmetic fundamentals makes handling more complex problems like decimal divisions accessible and straightforward.

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Most popular questions from this chapter

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