round of the following digits-
3.65*105(upto are place of decimal)
0.882026(upto three significant figures)
311.299(upto four significant figures)
4.783(upto two significant figures)
all will be rounded upward. I can check your work.
Now on the first, the common rule is if the estimated digit is 5, round up, and in the first one 3.7
However, this forces you to round up 5/9 of the time, and forces a bias upward. So some thinking texts change that rounding rule whken it is a 5, to round to the nearest even number.
examples 92.45 rounds to 92.4
90.5 rounds to 90
91.5 round to 92 and so on. If you are handling data, frankly this rule makes more sense. However, on student grades half the class doesn't like it, because their grades are rounded DOWN.
To round the given digits, follow these guidelines based on the desired precision:
1. To round 3.65 * 10^5 to the nearest tenth (up to one decimal place):
- Since there is only one significant figure (3), rounding to the nearest tenth means keeping the 5 in the next decimal place as it is.
- The rounded value is 3.7 * 10^5.
2. To round 0.882026 to three significant figures:
- Count the number of non-zero digits, which are 3 (8, 8, 2).
- The last significant figure is the 2, so we keep it and round the rest of the digits.
- The rounded value is 0.882.
3. To round 311.299 to four significant figures:
- Count the number of non-zero digits, which are 5 (3, 1, 1, 2, 9).
- Round the fifth digit (9) to the nearest value by looking at the next digit (if it is 5 or greater, round up; if it is less than 5, round down).
- The rounded value is 311.3.
4. To round 4.783 to two significant figures:
- Count the number of non-zero digits, which are 3 (4, 7, 8).
- The last significant figure is the 8, so we keep it and round the rest of the digits.
- The rounded value is 4.8.
Remember, when rounding, always consider the next digit to determine whether to round up or down.