Rounding

    • Rounding means estimating the exact value of a given number
    • With the exception of the smallest place occupied by a digit in a number, a number can be rounded to any place that its digits occupy such as the hundreds, ones, tenths, hundredths (rounding target)
    • The determination on whether a number is rounded up or down is based on the digit that occupies the place to the immediate right of the digit in the place that is the rounding target
    • If the digit to the immediate right is greater than or equal to 5 (≥ 5), then the digit in the place that is the rounding target is increased by 1 (rounded up); and if the digit to the immediate right is less than 5 (< 5), then the digit in the place that is the rounding target does not change (rounded down)
    • Notable mnemonic: 5 or more, raise the score–4 or less, let it rest
    • With respect to rounding to whole number places (…, hundreds, tens, ones), the digit or digits to the immediate right of the rounding target are changed to 0s
    • Example: 1,453 rounded to the nearest hundred (rounding target) is equal to 1,500
    • With respect to rounding to decimal number places (tenths, hundredths, thousandths,…), the digit or digits to the immediate right of the rounding target are dropped
    • Example: 4.463 rounded to the nearest tenth (rounding target) is equal to 4.5 since the digit to the immediate right of the tenths place (6) is greater than or equal to 5; and 4.463 rounded to the nearest hundredth (rounding target) is equal to 4.46 since the digit to the immediate right of the hundredths place (3) is less than 5
    • The smaller the rounding target is, the more precise or closer approximation of the exact value of a given number
    • Example: 23.458 rounded to the nearest hundredth (23.46) is more precise than 23.458 rounded to the nearest tenth (23.5) because the place value of the digit in the hundredths place (0.05) is smaller than the place value of the digit in the tenths place (0.4)
    • Rounding is useful to express an estimation of a non-terminating decimal number such as pi (π)
    • Like other currencies around the world, US Dollar amounts are often rounded to the nearest hundredth (two decimal places)
    • In other words, rounding is useful when the exact value of a number is not needed or known

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