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Visual Worksheet: Terminating and Repeating Decimals | Mathematics (Maths) Class 9 PDF Download

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FAQs on Visual Worksheet: Terminating and Repeating Decimals - Mathematics (Maths) Class 9

1. What are terminating decimals and how do they differ from repeating decimals?
Ans.Terminating decimals are decimal numbers that have a finite number of digits after the decimal point. For example, 0.75 and 2.5 are terminating decimals. On the other hand, repeating decimals have one or more digits that repeat infinitely. An example of a repeating decimal is 0.333..., where the digit 3 repeats indefinitely.
2. How can I determine if a fraction will result in a terminating or repeating decimal?
Ans.To determine if a fraction will result in a terminating or repeating decimal, you can look at the prime factorization of its denominator (after simplifying the fraction). If the only prime factors of the denominator are 2 and/or 5, the decimal representation will be terminating. If there are any other prime factors, the decimal will be repeating.
3. Can you provide examples of both terminating and repeating decimals?
Ans.Certainly! Examples of terminating decimals include 0.5 (which equals 1/2) and 0.25 (which equals 1/4). Examples of repeating decimals include 0.666... (which equals 2/3) and 0.142857... (which equals 1/7), where the sequences of digits repeat.
4. What is the significance of identifying terminating and repeating decimals in mathematics?
Ans.Identifying terminating and repeating decimals is significant in mathematics because it helps in understanding the behavior of numbers in calculations, particularly in division and fractions. Knowing whether a decimal terminates or repeats can also aid in estimating values and performing operations accurately.
5. How do I convert a repeating decimal into a fraction?
Ans.To convert a repeating decimal into a fraction, you can use the following steps: Let x equal the repeating decimal. Multiply x by a power of 10 that moves the decimal point to the right of the repeating part. Subtract the original x from this new equation to eliminate the repeating part. Solve for x to find the fractional representation. For example, to convert 0.333... to a fraction, you set x = 0.333..., then 10x = 3.333..., and subtract to get 9x = 3, leading to x = 1/3.
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