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Introduction to Decimals

How can we id...

Question

How can we identify that which decimal number is a rational number?

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Solution

If the decimal number is terminating or non-terminating recurring, then it is a rational number.

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Q. how can we write a decimal form of any random rational or irrational number?

Q. circumference of circle =2πr, so we can write π as circumference/diameter, which we know will be a rational number, so how can we say that π is an irrational number?

Q. Without actually performing the long division, we can state that the following rational number will have a non terminating decimal expansion.

\frac{129}{2^{2} 5^{7} 7^{5}}

Without actually performing the long division, we can state that the following rational number will have terminating decimal expansion.

\frac{35}{50}

Q. Any real number which has decimal expansion that terminates can be expressed as a rational number whose denominator is a power of 10.

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