2.32 as a fraction

Kana Ai Author

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30-12-2024

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Decoding 2.32: How to Express it as a Fraction

The decimal number 2.32 might seem simple, but converting it into a fraction requires understanding place value and a bit of arithmetic. Let's break down the process step-by-step.

Understanding Place Value

The decimal 2.32 has three distinct parts:

• 2: This represents two whole units.
• 0.3: This represents three-tenths (3/10).
• 0.02: This represents two-hundredths (2/100).

Converting to a Fraction

To convert 2.32 to a fraction, we need to combine these parts. Since the whole number part (2) is already a whole number, we only need to deal with the decimal part (0.32).

1. Write the decimal part as a fraction: 0.32 can be written as 32/100. This is because the last digit (2) is in the hundredths place.

2. Simplify the fraction: The fraction 32/100 can be simplified by finding the greatest common divisor (GCD) of 32 and 100. The GCD of 32 and 100 is 4. Dividing both the numerator and denominator by 4, we get:

   32 ÷ 4 = 8 100 ÷ 4 = 25

   So, 32/100 simplifies to 8/25.

3. Combine the whole number and the fraction: Now we combine the whole number (2) with the simplified fraction (8/25). This gives us the final answer:

   2 8/25

Therefore, 2.32 as a fraction is 2 8/25.

Alternative Method: Using Decimal Multiplication

Another approach is to multiply the decimal by a power of 10 to eliminate the decimal point. Since there are two digits after the decimal point, we multiply by 100:

2.32 x 100 = 232

This gives us the numerator of our fraction. The denominator is the power of 10 we used, which is 100. This gives us the improper fraction 232/100.

We can then simplify this fraction by dividing both the numerator and denominator by their GCD (which is 4):

232 ÷ 4 = 58 100 ÷ 4 = 25

This gives us 58/25. Converting this improper fraction to a mixed number, we divide 58 by 25:

58 ÷ 25 = 2 with a remainder of 8

So the mixed number is 2 8/25, confirming our earlier result.

In conclusion, both methods lead to the same answer: 2.32 expressed as a fraction is 2 8/25. Choosing the method that feels most comfortable and intuitive to you is perfectly acceptable.