Convert .66 to a fraction
The correct answer and explanation is:
Correct Answer:
0.66 as a fraction is 33/50.
Explanation (300 words):
To convert 0.66 to a fraction, you start by understanding what this decimal means. The decimal 0.66 represents 66 hundredths, which can be written as: 0.66=661000.66 = \frac{66}{100}
This fraction is correct, but it is not in its simplest form. We simplify fractions by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD) — the largest number that divides both numbers exactly.
For 66 and 100, the greatest common divisor is 2. So, we divide both parts of the fraction: 66÷2100÷2=3350\frac{66 \div 2}{100 \div 2} = \frac{33}{50}
Now we have the simplified fraction: 0.66=33500.66 = \frac{33}{50}
To verify that this is correct, we can convert the fraction back into a decimal: 3350=0.66\frac{33}{50} = 0.66
This confirms that the simplification was done correctly.
Why Simplify?
Simplifying a fraction makes it easier to understand and use. The simplest form of a fraction is the one where the numerator and denominator have no common divisors except 1. This helps when comparing, adding, or subtracting fractions in other math problems.
Note on Repeating Decimals:
It’s important to distinguish 0.66 (two decimal places) from 0.666… (a repeating decimal).
- 0.66 = 66/100 = 33/50
- 0.666… = 2/3, which is a different number (slightly larger than 0.66).
In summary, 0.66 is equal to the simplified fraction 33/50, and the process involves recognizing the place value, converting to a fraction with a power of 10 as the denominator, and simplifying using the GCD.