2.65 as a fraction

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31-03-2025

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Converting decimals to fractions might seem daunting, but it's a straightforward process once you understand the steps. Let's learn how to turn the decimal 2.65 into a fraction.

Understanding Decimals and Fractions

Decimals and fractions both represent parts of a whole. Decimals use a base-ten system (tenths, hundredths, thousandths, etc.), while fractions express parts as a ratio of a numerator (top number) and a denominator (bottom number).

Step 1: Write the Decimal as a Fraction over 1

Our starting point is 2.65. To begin the conversion, we write this as a fraction with a denominator of 1:

2.65/1

Step 2: Eliminate the Decimal Point

To remove the decimal point, we need to multiply both the numerator and the denominator by a power of 10. Since 2.65 has two decimal places, we'll multiply by 100 (10²):

(2.65 x 100) / (1 x 100) = 265/100

Step 3: Simplify the Fraction

Now, we simplify the fraction by finding the greatest common divisor (GCD) of the numerator (265) and the denominator (100). The GCD of 265 and 100 is 5.

Divide both the numerator and the denominator by 5:

265 ÷ 5 = 53

100 ÷ 5 = 20

This gives us our simplified fraction:

53/20

Step 4: Check Your Work

To verify our conversion, you can divide the numerator (53) by the denominator (20). You should get back the original decimal, 2.65.

2.65 as a Mixed Number

While 53/20 is a perfectly valid fraction, it's also possible to express it as a mixed number. A mixed number combines a whole number and a fraction.

To do this, divide 53 by 20:

53 ÷ 20 = 2 with a remainder of 13

This means 2.65 as a mixed number is:

2 13/20

Conclusion: 2.65 as a Fraction

Therefore, the decimal 2.65 can be expressed as both the improper fraction 53/20 and the mixed number 2 13/20. Both are correct representations, and the best choice depends on the context of your problem.

Frequently Asked Questions

How do I convert other decimals to fractions?

Follow the same steps outlined above. Multiply the decimal by a power of 10 to remove the decimal point, then simplify the resulting fraction.

What if the decimal has more than two decimal places?

If the decimal has three decimal places, multiply by 1000. For four decimal places, multiply by 10000, and so on. The key is to multiply by 10 raised to the power equal to the number of decimal places.

Why is simplifying the fraction important?

Simplifying makes the fraction easier to understand and work with. It presents the fraction in its most concise form.

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