• It provides the rounding method of the number according to decimal system

When certain number is closed with the number in n digits (1) or rounded n decimal places, arrange the number as follows.

• (1) When the number of (n+1) decimal places is less than 1/2 of 1 unit, it is rounded off. (See Example 1)
• When the number of (n+1) decimal places exceeds 1/2 of 1 unit, 1 unit is rounded up to n decimal places (See Example 2)
• (3) When the number of (n+1) decimal places is 1/2 of 1 unit of n decimal places or it is unknown if the number of (n+1) decimal places is rounded off or up, follow (a) or (b).
  • (a) If the number of n decimal places is 0, 2, 4, 6, 8, it is omitted (See Example 3)
  • (b) If the number of n decimal places is 1, 3, 5, 7, 9, the number of n decimal places is raised up 1 unit. (See Example 4)
• When it is knownn if the number of (n+1) decimal places is rounded off or up, it should follow the method in (1) or (2). (See Example 5)

  Remark

  • This rounding method should done at once. If we use example, when we close th5.346 with 2 effective digits, it becomes 5.3.
    This cannot be done by dividing twice like 5.347 = (first stage) 5.35 and (second stage) 5.4.

  Example 1

  • When we close 1.23 with 3 digits of effective number, it becomes 1.2 according to the method (1)
  • When closing 1.2344 with 3 digits of effective number, it becomes 1.23 according to method (1)
  • When closing 1.2344 with 3 digits below the decimal, it becomes 1.234 according to method (1)

  Example 2

  • When closing 1.26 with two digits of effective number, it becomes 1.3 according to method (2)
  • When closing 1.2501 with two digits of effective number, it becomes 1.3 according to method (2)
  • When closing 1.2967 with 3 digits of effective number, it becomes 1.30 according to method (2)
  • When closing 1.2967 with 3 digits below the decimal, it becomes 1.297 according to method (2)

  Example 3

  • When closing 0.105 (this number is known to have 5 in the 3rd place of effective number or it is not known if it is rounded off or up) with 2 digits of effective number, it becomes 0.10 according to method (3)(a)
  • When closing 1.450 (this number is known to have effective number in the 3rd place of effective number or it is not known if the second digit number is 1/2 of 1 unit or it is not known of it is rounded off or up) with two digits of effective number, it becomes 1.4 according to method (3)(a)
  • When closing 1.25 (this number is known to have 5 in the 3rd digit of effective number or it is not known if it is rounded off or up) with two digits of effective number, it becomes 1.2 according to the method (3)(a)
  • When closing 0.0625 (this number is known to have 5 in the 4th digit of effective number or it is not known if it is rounded off or up) with 3 places below decimal, it becomes 0.062 according to method (3)(a)

  Example 4

  • When closing 0.0955 (this number is known to have 5 in the 3rd digit of effective number or it is not known if it is rounded off or up) with 2 places below decimal, it becomes 0.096 according to method (3)(b)
  • When closing 1.350 (this number is known to have 1/2 of 1 unit of 2nd digit or it is not known if it is rounded off or up) with 2 digits of effective number, it becomes 1.4 according to method (3)(b).
  • When closing 1.15 (this number is known to have 5 in the 3rd digit of effective number or it is not known if it is rounded off or up) with 2 digits of effective number, it becomes 1.2 according to method (3)(b)
  • When closing 0.095 (this number is known to have 5 in the 3 places below decimal or it is not known if it is rounded off or up) with 2 places below decimal, it becomes 0.10 according to method (3)(b)

  Example 5

  • When closing 2.35 (this number is known to be rounded up from 2.347) with 2 digits of effective number, it becomes 2.3 according to method (1)
  • When closing 2.45 (this number is known to be rounded off from 2.452) with 2 digits of effective number, it becomes 2.54 according to method (2)
  • When closing 4.184 (this number is known to be round off from 4.1852) with 3 places below decimal, it becomes 4.19 according to method (2)