Round-off a number to a given number of significant digits
Given a positive number n (n > 1), round-off this number to a given no. of significant digits, d.
Input : n = 139.59 d = 4 Output : The number after rounding-off is 139.6 . The number 139.59 has 5 significant figures and for rounding-off the number to 4 significant figures, 139.59 is converted to 139.6 . Input : n = 1240 d = 2 Output : The number after rounding-off is 1200 .
What are significant figures?
Each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first non-zero digit, are called as significant figures.
Since there are numbers with large number of digits, for example, = 3.142857143, so in order to limit such numbers to a manageable number of digits, we drop unwanted digits and this process is called rounding off.
Significant digits include all the digits in a number falling in one of the following categories –
- All non-zero digits.
- Zero digits which-
- lie between significant digits.
- lie to the right of decimal point and at the same time to the right of a non-zero digit.
- are specifically indicated to be significant.
The following table shows numbers and no. of significant digits present in them –
Rules for Rounding-off a Number
To round off a number to n significant figures-
- Discard all digits to the right of nth significant digit.
- If this discarded number is-
- less than half a unit in nthplace, leave the nth digit unchanged.
- greater than half a unit in the nth place, increase the nth digit by unity.
- exactly half a unit in the nth place, increase the nth digit by unity if its odd, otherwise leave it unchanged.
The following table shows rounding-off a number to a given no. of significant digits –
The number after rounding-off is 139.6
Time complexity: O(logN)
Space complexity: O(1)
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