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Chapter 5: Problem 36

Divide. $$3.2 \div 0.001$$

Short Answer

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Step by step solution

01

Understand the Problem

The problem is to divide 3.2 by 0.001. In mathematical notation, this can be written as \(3.2 \div 0.001\).
02

Convert Division to Multiplication

Division can be converted to multiplication by the reciprocal. So, \(3.2 \div 0.001\) becomes \(3.2 \times \frac{1}{0.001}\).
03

Calculate the Reciprocal

The reciprocal of 0.001 is \frac{1}{0.001} = 1000\. So now we have \(3.2 \times 1000\).
04

Perform the Multiplication

Multiply 3.2 by 1000. \(3.2 \times 1000 = 3200\).
05

Obtain the Final Answer

The result of the division \(3.2 \div 0.001\) is therefore 3200.

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Key Concepts

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

Reciprocal
Understanding the reciprocal is key when converting division problems into multiplication problems. A reciprocal of a number is simply that number flipped upside down. For instance, the reciprocal of 2 is \(\frac{1}{2} \). This holds true for decimals as well. To find the reciprocal of 0.001, you place 1 over 0.001, which results in \(\frac{1}{0.001} = 1000 \). When you understand reciprocals, you're better equipped to tackle division problems.
Multiplication
Multiplication plays a key role in solving division by decimals. Once you've converted the division problem into multiplication using the reciprocal, you proceed with the standard multiplication operation. For example, converting \(3.2 \div 0.001 \) to \(3.2 \times 1000 \) simplifies the problem significantly. In this case, multiplying 3.2 by 1000, you get 3200. Always ensure to line up decimal points correctly to avoid mistakes.
Arithmetic Operations
Arithmetic operations include addition, subtraction, multiplication, and division. Understanding how these operations interact with each other is crucial for solving complex problems. Division by a decimal can often seem tricky, but converting it into multiplication by using the reciprocal simplifies the process. First, understand what the problem is asking. Next, make use of the reciprocal to transform the operation into multiplication. Finally, perform the multiplication step and arrive at the solution. This structured approach will make arithmetic operations far less daunting.

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