This is a terminating decimal. Convert the fraction 7 12 to a decimal. The bar over the number, in this case 3 , indicates the number or block of numbers that repeat unendingly. See also Converting Repeating Decimals to Fractions. The best answer I can give is take the top numerator and divide it by the bottom denominator. Also, anytime there is a fraction with a 9, 99, , etc. Now, notice that the ones that terminate can be changed to tenths, hundredths, thousandths, etc.
The ones that do not terminate cannot be changed to tenths, hundredths, thousandths, etc. Hint: If you first reduce the fraction to lowest terms, the numbers will be smaller and the division will be a bit easier as a result.
First reduce the fraction to lowest terms. It consists only of twos. It consists only of twos and fives. The zero remainder terminates the process. If the prime factorization of the resulting denominator does not consist strictly of twos and fives, then the division process will never have a remainder of zero. However, repeated patterns of digits must eventually reveal themselves. This will indicate repetition is beginning. Note the second appearance of 4 as a remainder in the division above.
This is an indication that repetition is beginning. It is easy to see that all terminating decimals can be converted to a fraction of this form.
Several examples are. From these representations, we are pretty confident that all terminating decimals can be expressed as. But notice that and are also terminating decimals, so we can also conjecture that maybe, fractions with denominators of 2 and 5 are terminating decimals. Intuition tells us that they are indeed.
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