How Does Rounding Decimals & Whole Numbers Compare?
In mathematics, rounding is a procedure in which some of the non-zero digits are dropped or converted to zero, to facilitate estimation or simplify record keeping. Long streams of digits may be unwieldy, so all digits to the right of a certain point are dropped, or converted to zero. The digits that are eliminated are unimportant, because their place value is too small to be significant. Rounding makes it easier to perform operations with very large whole numbers and very small decimals, and allows you to convert the numbers to scientific notation.
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Rounding Whole Numbers
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To round a whole number, choose the smallest place value that is significant. If the digit to the immediate right of that place value is less than five, then convert the digit to the right and all others past it to zero. If the digit to the right of the least significant place value is five or greater, then add one to the number in the significant place value, and convert all digits to the right of it to zero.
Rounding Versus Truncation
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The treatment of the digit in the least significant place value is what differentiates rounding from truncation. In truncation, the digit in that position is not changed, regardless of the value of the adjacent digit. Rounding is usually preferred to truncation, because the errors in rounding will be random and will tend to balance out, while truncation will always yield a lower result than the actual number.
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Rounding a Decimal
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Rounding a decimal is almost identical to rounding a whole number. The main difference is that the digits to the right of the least significant place value are dropped instead of being converted to zero. Trailing zeroes are always dropped in decimals, since otherwise the decimal could go on indefinitely.
Irrational Numbers and Repeating Decimals
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Though rounding is a convenience when dealing with large whole numbers, it is a necessity when dealing with some decimals. Irrational numbers, such as pi and many square roots, must be rounded or truncated, or else the digits would extend infinitely. Pi has been calculated to 200 billion decimal places, but that is hardly useful for most calculations. Repeating square roots are frequently rounded as well. In these cases, shortening the number of digits is unavoidable.
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References
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