A terminating decimal is a decimal that has digits that doesn't go on forever. A terminating decimal is the same thing as a rational number, and doesn't repeat forever. Three examples of fractions with decimal representations that terminate are 1/8, 2/10, and 1/4. The decimal representation of 1/8 is equal to 0.125, which is terminating because the decimal values don't go on forever. The decimal representation of 2/10 is equal 0.2, which is terminating because the decimal values don't go on forever. The decimal representation of 1/4 is equal to 0.25, which is terminating because the decimal values don't go on forever.
2. Give three examples of fractions with decimal representations that repeat:
A repeating decimal is when the decimal values of the number goes on forever, or infinitely. Three examples of fractions with decimal representations that repeat are 1/3, 1/11, and 2/9. The decimal representation of 1/3 is 0.3333333...... (3 repeating on forever). This is an example of a repeating decimal because the three goes on forever. The decimal representation of 1/11 is 0.090909...... (09 repeating on forever). This is an example of a repeating decimal because the three goes on forever. The decimal representation of 2/9 is 0.222222...... (2 repeating on forever). This is an example of a repeating decimal because the three goes on forever. Usually, repeating decimals are shown with a bar over the number or numbers that are getting repeated.
3. Give three examples of irrational numbers, including one irrational number greater than 5:
An irrational number is a number that cannot be expressed as a ratio or a fraction. Three examples of irrational numbers, including one that is greater than 5, are √27, √30, and √34. The square root of 27 is approximately (fraction estimate) 5.196. The square root of 30 is approximately 5.477. The square root of 34 is approximately 5.8309. But remember that these square roots have no ends and the answers that I gave were just estimates.
4. How can you determinate whether you can write a given decimal as a fraction:
You can determine whether you can write a given decimal as a fraction by looking at it. You automatically know that a decimal can be represented as a fraction if it is either terminating or rational. You also know that if something irrational, that it CAN'T be written as a fraction. If a fraction neither repeats nor terminates, you automatically know that it can't be written as a fraction, which means that it is irrational. When looking at the terminating decimal, you can look at the place value in which the last number is in. For example, let's use 0.02. THe 2 is in the hundredths place, so the fraction is 2/100. You could also guess and check to make the decimal a fraction.
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