you know that 1/7= 0./142852.can u predict what the decimal expansion of 2/7,3/7,4/7,5/7,6/7,are ,are without actually doing the long devision?if so how.
Yes, the decimal expansions of 2/7, 3/7, 4/7, 5/7, and 6/7 can be predicted without actually doing long division. Here's how:
1. The decimal expansion of 1/7 is 0.142857 (repeating).
2. To find the decimal expansion of 2/7, we can double the decimal expansion of 1/7. This gives us 0.285714 (repeating).
3. To find the decimal expansion of 3/7, we can add the decimal expansion of 1/7 and 2/7. This gives us 0.428571 (repeating).
4. To find the decimal expansion of 4/7, we can double the decimal expansion of 2/7. This gives us 0.571428 (repeating).
5. To find the decimal expansion of 5/7, we can subtract the decimal expansion of 2/7 from 1. This gives us 0.714285 (repeating).
6. To find the decimal expansion of 6/7, we can subtract the decimal expansion of 1/7 from 1. This gives us 0.857142 (repeating).
Therefore, the decimal expansions of 2/7, 3/7, 4/7, 5/7, and 6/7 are 0.285714 (repeating), 0.428571 (repeating), 0.571428 (repeating), 0.714285 (repeating), and 0.857142 (repeating), respectively.
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Yes, the decimal expansions of 2/7, 3/7, 4/7, 5/7, and 6/7 can be predicted without actually doing long division. Here's how:
1. The decimal expansion of 1/7 is 0.142857 (repeating).
2. To find the decimal expansion of 2/7, we can double the decimal expansion of 1/7. This gives us 0.285714 (repeating).
3. To find the decimal expansion of 3/7, we can add the decimal expansion of 1/7 and 2/7. This gives us 0.428571 (repeating).
4. To find the decimal expansion of 4/7, we can double the decimal expansion of 2/7. This gives us 0.571428 (repeating).
5. To find the decimal expansion of 5/7, we can subtract the decimal expansion of 2/7 from 1. This gives us 0.714285 (repeating).
6. To find the decimal expansion of 6/7, we can subtract the decimal expansion of 1/7 from 1. This gives us 0.857142 (repeating).
Therefore, the decimal expansions of 2/7, 3/7, 4/7, 5/7, and 6/7 are 0.285714 (repeating), 0.428571 (repeating), 0.571428 (repeating), 0.714285 (repeating), and 0.857142 (repeating), respectively.
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