What is 4/3 as a decimal?
The fraction 4/3 represents four divided by three. To convert this fraction into a decimal, you simply perform the division.
Here's how to do it:
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Divide the numerator (4) by the denominator (3): 4 ÷ 3 = 1.333333...
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The result is a repeating decimal: 1.333333... The '3' repeats infinitely.
Therefore, 4/3 as a decimal is 1.333333... (or 1.33 recurring).
Why is it a repeating decimal?
When a fraction cannot be simplified to a fraction where the denominator is a power of 10 (like 10, 100, 1000, etc.), it results in a repeating decimal. This is because the division process continues indefinitely, creating a repeating pattern of digits.
How to represent repeating decimals?
There are two common ways to represent repeating decimals:
- Using a bar notation: Place a bar over the repeating digits. For example, 1.333333... is written as 1.3
- Using ellipsis: Write the decimal with a few repeating digits and add an ellipsis (...) at the end to indicate the repetition. For example, 1.333333...
Practical applications of converting fractions to decimals
Converting fractions to decimals is essential in many areas:
- Calculations: Decimal numbers are easier to work with in calculations, especially with calculators and computers.
- Measurement: Many measurements, like lengths and weights, are expressed in decimal units.
- Data analysis: Decimal numbers are often used to represent data in graphs and tables.
Conclusion
Converting 4/3 to a decimal results in a repeating decimal, 1.333333... (or 1.33 recurring). Understanding how to convert fractions to decimals and represent repeating decimals is a valuable skill in many fields.