(Decimals into Fractions) 0.65=? Please turn 0.65 into a Fraction and simplify to the lowest point you can.

The Correct Answer and Explanation is:

✅ Answer:

0.65 = 13/20 (simplified to lowest terms)

📘 Explanation

To convert a decimal like 0.65 into a fraction, follow these steps:

Step 1: Understand the Decimal

The decimal 0.65 means 65 hundredths, which can be written as:0.65=651000.65 = \frac{65}{100}0.65=10065

This is because the digits 6 and 5 are in the tenths and hundredths place, respectively.

Step 2: Simplify the Fraction

We now need to simplify the fraction 65100\frac{65}{100}10065. To do this, find the greatest common divisor (GCD) of the numerator and the denominator.

Factors of 65: 1, 5, 13, 65
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

The largest common factor is 5.

Now divide both the numerator and denominator by 5:65÷5100÷5=1320\frac{65 \div 5}{100 \div 5} = \frac{13}{20}100÷565÷5=2013

✅ Final Answer:

0.65=1320\boxed{0.65 = \frac{13}{20}}0.65=2013

Why Simplify?

Simplifying a fraction gives us the most reduced form, meaning the numerator and denominator have no common factors besides 1. It makes the fraction easier to understand and compare with others.

Additional Tip:

For any decimal that ends (is terminating), you can turn it into a fraction by:

Counting how many decimal places it has.
Placing the digits over 10, 100, 1000, etc., depending on the number of decimal places.
Simplifying.

For 0.65 (which has two decimal places), we put it over 100:0.65=65100=13200.65 = \frac{65}{100} = \frac{13}{20}0.65=10065=2013

This method works for any terminating decimal.

Conclusion:
0.65 as a simplified fraction is 13/20. This process helps build number sense and is fundamental for understanding more complex math like ratios, percentages, and algebra.