Final answer:
To convert 0.64 to a fraction, multiply both the numerator and denominator by 100 to remove the decimal point. Simplify the resulting fraction to get the answer. There are no repeating digits in 0.64 as a fraction.
Step-by-step explanation:
To convert 0.64 to a fraction, multiply both the numerator and the denominator by 100 to remove the decimal point. This gives us 64/100. We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4. So, 64/100 simplifies to 16/25. In this fraction, there are no repeating digits since the decimal part terminates.
To convert 0.64 with a bar to a fraction, you use algebraic methods to find that it equals 64/99, and there are two repeating digits, '6' and '4'.
To convert the decimal 0.64 with a bar over the digits to a fraction, we recognize that this represents the repeating decimal 0.646464... To convert this into a fraction, we can use the following method:
Let x = 0.6464..., then 100x = 64.6464... Subtracting these two equations:
100x = 64.6464...
x = 0.6464...
We obtain:
99x = 64, and therefore x = 64/99. This is the fraction equivalent of the repeating decimal 0.64 with a bar.
As for the number of repeating digits, there are two repeating digits in 0.64 with a bar, which are '6' and '4'.