2.3 repeating as a fraction or percentage​

2.3 repeating as a fraction or percentage​

The Correct Answer and Explanation is :

To express (2.3) repeating (denoted as (2.3\overline{3})) as a fraction, follow these steps:

Step 1: Set up the equation

Let (x = 2.3\overline{3}).

Step 2: Multiply to eliminate the repeating part

Since the repeating digit is “3,” multiply both sides of the equation by (10) to shift the decimal point:

[
10x = 23.3\overline{3}
]

Step 3: Set up another equation

Now, subtract the original (x) from this new equation:

[
10x – x = 23.3\overline{3} – 2.3\overline{3}
]

This simplifies to:

[
9x = 21
]

Step 4: Solve for (x)

To find (x), divide both sides by (9):

[
x = \frac{21}{9}
]

Step 5: Simplify the fraction

Now, simplify (\frac{21}{9}):

[
x = \frac{7}{3}
]

So, (2.3\overline{3} = \frac{7}{3}) as a fraction.

Converting to Percentage

To convert the fraction to a percentage, divide (7) by (3):

[
7 \div 3 \approx 2.3333
]

Now, to express it as a percentage, multiply by (100):

[
2.3333 \times 100 \approx 233.33\%
]

Summary

Thus, the repeating decimal (2.3\overline{3}) can be expressed as the fraction (\frac{7}{3}) and is approximately (233.33\%) when converted to a percentage.

This process illustrates the connection between repeating decimals, fractions, and percentages, highlighting the importance of understanding the relationships between different numerical representations. It demonstrates that many decimals, especially repeating ones, can be expressed precisely as fractions, which can then be further translated into percentage form for easier interpretation in real-world applications, such as finance, statistics, and everyday calculations.