1 year, 5 months ago
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If the decimals of a number x are rounded at place k after the decimal point...
what can we say about the decimal representation of x^2 or sqrt(x) ?
In other words, up to which digit of x^2 or sqrt(x), the resulting number is accurate?
In other words, up to which digit of x^2 or sqrt(x), the resulting number is accurate?
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M$1 Answer
When squaring a number x rounded at place k, the resulting number is accurate to k + 1 places after the decimal point.
When taking the squareroot of a number x rounded at place k, the resulting number is accurate to k - 1 places after the decimal point.
Example:
5/68 = 0.0735294...
If we round 3 places after the decimal point we get 0.074 rounded up from 0.0735...
Square 0.074 and we get: 0.005476
Square 5/68 and we get : 0.005406..
Accuracy is provided up to 4 places after the decimal point.
The squareroot of 5/68 is: 0.271...
The squareroot of 0.074 is: 0.272...
Here accuracy is provided up to 2 places after the decimal point.
When taking the squareroot of a number x rounded at place k, the resulting number is accurate to k - 1 places after the decimal point.
Example:
5/68 = 0.0735294...
If we round 3 places after the decimal point we get 0.074 rounded up from 0.0735...
Square 0.074 and we get: 0.005476
Square 5/68 and we get : 0.005406..
Accuracy is provided up to 4 places after the decimal point.
The squareroot of 5/68 is: 0.271...
The squareroot of 0.074 is: 0.272...
Here accuracy is provided up to 2 places after the decimal point.
You can leave an optional "tip" with Mahalo's virtual currency, Mahalo Dollars. If you are asking a difficult question that might require some research, or if you'd like a wide variety of feedback, a higher tip often leads to more answers to your question.
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