Which Is The Decimal Expansion Of 7/22?
The decimal expansion of 7/22 is 0.31818181818181818…. This is a repeating decimal, which means that the sequence of digits 318 repeats infinitely.
To find the decimal expansion of 7/22, we can use long division.
7 / 22 = 0.31818181818181818... The quotient is 0.3, and the remainder is 7. We then bring down the next digit of the dividend, which is 2. This gives us the following:
7 / 22 = 0.3 | 27 We divide 27 by 22, which gives us 1.2272727272727272… We then bring down the next digit of the dividend, which is 0. This gives us the following:
7 / 22 = 0.3 | 270 We divide 270 by 22, which gives us 12.272727272727272… We then bring down the next digit of the dividend, which is 0. This gives us the following:
7 / 22 = 0.3 | 2700 We divide 2700 by 22, which gives us 122.72727272727272… We then bring down the next digit of the dividend, which is 0. This gives us the following:
7 / 22 = 0.3 | 27000 We divide 27000 by 22, which gives us 1227.2727272727272… We then bring down the next digit of the dividend, which is 0. This gives us the following:
7 / 22 = 0.3 | 270000 We divide 270000 by 22, which gives us 12272.727272727272… We then bring down the next digit of the dividend, which is 0. This gives us the following:
7 / 22 = 0.3 | 2700000 We divide 2700000 by 22, which gives us 122727.27272727272… We then bring down the next digit of the dividend, which is 0. This gives us the following:
7 / 22 = 0.3 | 27000000 We continue dividing in this way, and we see that the remainder is always 318. Therefore, the decimal expansion of 7/22 is 0.31818181818181818….
Questions
- Why is the decimal expansion of 7/22 a repeating decimal?
The decimal expansion of 7/22 is a repeating decimal because the denominator of 7/22 is not divisible by 2, 5, or any other prime number greater than 5.
- What is the pattern of the repeating digits in the decimal expansion of 7/22?
The pattern of the repeating digits in the decimal expansion of 7/22 is 318.
- How can we find the decimal expansion of a fraction without using long division?
We can use a calculator or a computer to find the decimal expansion of a fraction. We can also use the following formula:
decimal expansion = numerator / denominator * 10^n where n is the number of digits to the right of the decimal point.
For example, to find the decimal expansion of 7/22 to three decimal places, we would use the following formula:
decimal expansion = 7 / 22 * 10^3 decimal expansion = 0.31818181818181818... 