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Chapter 1: Problem 67

\(\frac{4}{7}\)

Short Answer

Expert verified
The decimal equivalent of the fraction \( \frac{4}{7} \) is approximately 0.571.

Step by step solution

01

Identify the Fraction

Identify the fraction that needs to be converted to a decimal. In this case, the fraction is \( \frac{4}{7} \).
02

Perform Division

Perform the division operation to convert the fraction to a decimal. This implies dividing the numerator (4) by the denominator (7).
03

Calculation

Perform the division to get the decimal equivalent.
04

Result

Write down the result of the division. If possible, round off the decimal to a required number of decimal places.

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Key Concepts

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

Understanding Numerator and Denominator
When we talk about fractions, we often hear the terms "numerator" and "denominator". These are the two numbers that make up a fraction. Let's break them down:

  • Numerator: This is the number on the top of the fraction. It shows how many parts of a whole you have.
  • Denominator: This is the number at the bottom of the fraction. It tells you how many equal parts the whole is divided into.
Consider the fraction \( \frac{4}{7} \). Here, 4 is the numerator, meaning we have 4 parts. The number 7 is the denominator, representing the 7 parts into which our whole is divided. Together, they create a simple fraction that can be expressed in other forms, such as decimals.
Performing Division Operation
Converting a fraction to a decimal involves a division operation. This might sound a bit technical, but it's simpler than it seems. Here's what you need to do:

To convert the fraction \( \frac{4}{7} \) into a decimal, you perform a division where you divide the numerator by the denominator. In mathematical terms, we calculate \( 4 \div 7 \).

Although this division sometimes means dealing with long division or getting a result that goes on forever, the process is straightforward. You'll usually arrive at a repeating or terminating decimal. For practice, you can use a calculator to make sure your manual calculations match the electronic result.
Importance of Rounding Decimals
Once you have your decimal result from dividing, it might show a long series of numbers. Not all situations require such precision, which is why rounding decimals can be very handy.

Rounding helps simplify and make sense of numbers by reducing them to an understandable length. Let's say dividing 4 by 7 gives you 0.57142857. Depending on the precision you need, you could round this to 0.57 for two decimal places, or 0.571 for three.

Here's a quick tip on how to round:
  • Decide how many decimal places you need.
  • Look at the next digit 鈥� if it's 5 or more, round up; if it's less than 5, round down.
By rounding, you retain the most valuable parts of your calculation, making it easy to read and understand by anyone reviewing your work.

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Most popular questions from this chapter

\(\frac{3 \cdot 6-4 \cdot 6}{5+1}\)

\(5\left(\frac{1}{5}\right) \neq 0\)

\(300\left(1+\frac{0.1}{12}\right)^{24}\)

\((14-17) \cdot(13-19)\)

\(25-32 \div 4\)
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