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How to find the reciprocal of a decimal?

Understand the Problem

The question is asking how to find the reciprocal of a decimal number, which involves taking the value of 1 divided by that decimal. This concept is fundamental in mathematics and can be solved by using simple arithmetic.

Answer

The reciprocal of $0.5$ is $2$.
Answer for screen readers

The reciprocal of the decimal number $0.5$ is $2$.

Steps to Solve

  1. Identify the decimal number

Let's say we have a decimal number, for example, 0.5. Identify what decimal you need to work with to find its reciprocal.

  1. Set up the reciprocal calculation

To find the reciprocal of the decimal number, set up the equation using the decimal. The reciprocal is calculated by dividing 1 by that decimal.

For 0.5, it would be:

$$ \text{Reciprocal} = \frac{1}{0.5} $$

  1. Perform the division

Now, calculate the value of the division. Remember that dividing by a decimal can be converted to multiplying by a fraction. For this case:

$$ \frac{1}{0.5} = \frac{1 \times 2}{0.5 \times 2} = \frac{2}{1} $$

This simplifies the calculation.

  1. Express the final result

The result of the calculation will give you the reciprocal. In our example:

$$ \text{Reciprocal} = 2 $$

The reciprocal of the decimal number $0.5$ is $2$.

More Information

Finding the reciprocal of a decimal is often useful in various mathematical calculations, such as solving equations or working with fractions. It’s essential to understand that the reciprocal of any non-zero number $x$ is given by $\frac{1}{x}$.

Tips

  • Forgetting to divide correctly when working with decimals. Convert decimals into fractions to simplify calculations.
  • Confusing reciprocal with multiplication or trying to multiply the number instead of dividing by it.
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