This is a really good question. 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. Ask a question for free Get a free answer to a quick problem.
You start with a single dot in the ones box:. Picture 1: When you unexplode the first dot, you get 10 dots in the box, which gives one group of six with remainder of 4. Picture 2: When you unexplode those four dots, you get 40 dots in the box, which gives six group of six with remainder of 4.
Since the remainder repeated we got a remainder of 4 again , we can see that the process will now repeat forever:. Write a convincing argument that:. Skip to content Place Value and Decimals. Definition A unit fraction is a fraction that has 1 in the numerator. Try some more examples on your own. Do you have a conjecture? Problem 7 Complete the table below which shows the decimal expansion of unit fractions where the denominator is a power of 2. Fraction Denominator Decimal.
Problem 8 Complete the table below which shows the decimal expansion of unit fractions where the denominator is a power of 5. If Marcus had the unit fraction , what would be his first step to turn it into a decimal?
What would the decimal expansion look like and why? Now think about unit fractions with powers of 5 in the denominator. Problem 9 Complete the statement below by filling in the numerator of the fraction. Problem 10 Write a statement about the decimal representations of unit fractions and justify that your statement is correct. Problem 11 Each of the fractions listed below has a terminating decimal representation.
Definition The period of a repeating decimal is the smallest number of digits that repeat. Problem 12 Complete the table below which shows the decimal expansion of unit fractions where the denominator has prime factors besides 2 and 5. Instructors are independent contractors who tailor their services to each client, using their own style, methods and materials.
Terminating and Repeating Decimals Any rational number that is, a fraction in lowest terms can be written as either a terminating decimal or a repeating decimal. Example 1: Convert the fraction 5 8 to a decimal. Example 2: Convert the fraction 7 12 to a decimal. Subjects Near Me. Download our free learning tools apps and test prep books.
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