Class 9 Exam > Class 9 Questions > You know that 1/7 = 0.142857 . can you predic...
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You know that 1/7 = 0.142857 . can you predict what the decimal expansions of 2/3 , 3/7, 4/7, 5/7, 6/7 are ,without actually doing the long division ? if so, how?
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You know that 1/7 = 0.142857 . can you predict what the decimal expans...
2/7= 2×1/7= 0.285714, 3/7= 3×1/7= 0.428571, 4/7=4×1/7 = 0.571428, 5/7=5×1/7= 0.714285, 6/7=6×1/7= 0.857142
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You know that 1/7 = 0.142857 . can you predict what the decimal expans...
Understanding the Pattern of Decimal Expansions
1. Understanding the pattern of decimal expansions of 1/7:
To predict the decimal expansions of fractions without performing long division, we can observe the pattern in the decimal expansion of 1/7. By dividing 1 by 7, we obtain the following decimal expansion: 0.142857142857...
2. Multiplying the decimal expansion by 2:
To find the decimal expansion of 2/7, we can multiply the decimal expansion of 1/7 by 2. This is because multiplying the numerator by 2 will result in doubling the value of the fraction. Therefore, we have:
2 × 0.142857142857... = 0.285714285714...
3. Multiplying the decimal expansion by 3:
Similarly, to find the decimal expansion of 3/7, we can multiply the decimal expansion of 1/7 by 3. This is because multiplying the numerator by 3 will result in tripling the value of the fraction. Therefore, we have:
3 × 0.142857142857... = 0.428571428571...
4. Multiplying the decimal expansion by 4:
To find the decimal expansion of 4/7, we can multiply the decimal expansion of 1/7 by 4. This is because multiplying the numerator by 4 will result in quadrupling the value of the fraction. Therefore, we have:
4 × 0.142857142857... = 0.571428571428...
5. Multiplying the decimal expansion by 5:
To find the decimal expansion of 5/7, we can multiply the decimal expansion of 1/7 by 5. This is because multiplying the numerator by 5 will result in quintupling the value of the fraction. Therefore, we have:
5 × 0.142857142857... = 0.714285714285...
6. Multiplying the decimal expansion by 6:
Lastly, to find the decimal expansion of 6/7, we can multiply the decimal expansion of 1/7 by 6. This is because multiplying the numerator by 6 will result in six times the value of the fraction. Therefore, we have:
6 × 0.142857142857... = 0.857142857142...
With this approach, we can predict the decimal expansions of 2/3, 3/7, 4/7, 5/7, and 6/7 without performing long division. By understanding the pattern in the decimal expansion of 1/7 and applying multiplication to the decimal expansion, we can quickly obtain the decimal representations of these fractions.
1. Understanding the pattern of decimal expansions of 1/7:
To predict the decimal expansions of fractions without performing long division, we can observe the pattern in the decimal expansion of 1/7. By dividing 1 by 7, we obtain the following decimal expansion: 0.142857142857...
2. Multiplying the decimal expansion by 2:
To find the decimal expansion of 2/7, we can multiply the decimal expansion of 1/7 by 2. This is because multiplying the numerator by 2 will result in doubling the value of the fraction. Therefore, we have:
2 × 0.142857142857... = 0.285714285714...
3. Multiplying the decimal expansion by 3:
Similarly, to find the decimal expansion of 3/7, we can multiply the decimal expansion of 1/7 by 3. This is because multiplying the numerator by 3 will result in tripling the value of the fraction. Therefore, we have:
3 × 0.142857142857... = 0.428571428571...
4. Multiplying the decimal expansion by 4:
To find the decimal expansion of 4/7, we can multiply the decimal expansion of 1/7 by 4. This is because multiplying the numerator by 4 will result in quadrupling the value of the fraction. Therefore, we have:
4 × 0.142857142857... = 0.571428571428...
5. Multiplying the decimal expansion by 5:
To find the decimal expansion of 5/7, we can multiply the decimal expansion of 1/7 by 5. This is because multiplying the numerator by 5 will result in quintupling the value of the fraction. Therefore, we have:
5 × 0.142857142857... = 0.714285714285...
6. Multiplying the decimal expansion by 6:
Lastly, to find the decimal expansion of 6/7, we can multiply the decimal expansion of 1/7 by 6. This is because multiplying the numerator by 6 will result in six times the value of the fraction. Therefore, we have:
6 × 0.142857142857... = 0.857142857142...
With this approach, we can predict the decimal expansions of 2/3, 3/7, 4/7, 5/7, and 6/7 without performing long division. By understanding the pattern in the decimal expansion of 1/7 and applying multiplication to the decimal expansion, we can quickly obtain the decimal representations of these fractions.
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You know that 1/7 = 0.142857 . can you predict what the decimal expansions of 2/3 , 3/7, 4/7, 5/7, 6/7 are ,without actually doing the long division ? if so, how?
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You know that 1/7 = 0.142857 . can you predict what the decimal expansions of 2/3 , 3/7, 4/7, 5/7, 6/7 are ,without actually doing the long division ? if so, how? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about You know that 1/7 = 0.142857 . can you predict what the decimal expansions of 2/3 , 3/7, 4/7, 5/7, 6/7 are ,without actually doing the long division ? if so, how? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for You know that 1/7 = 0.142857 . can you predict what the decimal expansions of 2/3 , 3/7, 4/7, 5/7, 6/7 are ,without actually doing the long division ? if so, how?.
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