Using ISO Rounding

• Using ISO Rounding
  • Condition for Applying ISO Rounding
  • The Input Value must be at the Half-way point between the Increment
  • Applying ISO Rounding based upon Increment Size
  • The Increment should be an Order of 10
  • Increment of 1
  • Increment of 2
  • Increment of 5
  • Applying ISO Rounding
  • ASTM/ISO Standard for Rounding

ISO rounding applies to the rounding algorithms used for rounding analytes.

Condition for Applying ISO Rounding

The Input Value must be at the Half-way point between the Increment

ISO rounding comes into play when the digits from the last significant figure onwards are exactly at the half-way point between the increment, that is, where the value to round is exactly half way between the significant figures based on the picture and the increment number.

For example, where the input is 12.3456 and the mask is ##.##, then, as the value is not exactly 12.345, ISO rounding cannot be applied so the default rounding rules are applied.

Applying ISO Rounding based upon Increment Size

The Increment should be an Order of 10

If the increment is not an order of 10 (that is, 1, 10, 100, 1000, etc.), then whatever comes out of the logic stands. It does not make sense to have ISO rounding active when the increment is not an order of 10. This is demonstrated below.

The increment controls how the least significant digits are managed after rounding. An increment of 1 dictates that the number is not changed at all, whereas an increment of 10 takes the least significant digits to the nearest 10.

For example, the rounded number 1.345 becomes 1.350 after applying an increment of 10.

The same rules apply if exponential notation is required, however, the rules are applied to the mantissa component of the number only. The exponent is not given leading zeros if the mask size exceeds that of the exponent value.

Increment of 1

When the increment is 1, the last significant figure needs to be a digit of 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9.

Examples of when the increment is 1 and rounding to two significant figures:

• 1.234 --> this is not half-way between increments 1.23 and 1.24 so normal rounding --> round to closest increment using two significant figures --> 1.23
• 1.235 --> This is half-way between increments 1.23 and 1.24 so ISO rounding --> 3 is odd so round to previous increment using two significant figures --> 1.23
• 1.236 --> this is not half-way between increments 1.23 and 1.24 so normal rounding --> round to closest increment using two significant figures --> 1.24
• 1.244 --> this is not half-way between increments 1.24 and 1.25 so normal rounding --> round to closest increment using two significant figures --> 1.24
• 1.245 --> This is half-way between increments 1.24 and 1.25 so ISO rounding --> 4 is odd so round to next increment using two significant figures --> 1.25
• 1.246 --> this is not half-way between increments 1.24 and 1.25 so normal rounding --> round to closest increment using two significant figures --> 1.25

Increment of 2

When the increment is 2, the last significant figure needs to be a digit of 0, 2, 4, 6 or 8.

Examples of when the increment is 2 and rounding to two significant figures:

• 1.22 --> this already at an increment --> 1.22
• 1.224 --> this is not half-way between increments 1.22 and 1.24 so normal rounding --> round to closest increment using two significant figures --> 1.22
• 1.226 --> this is not half-way between increments 1.22 and 1.24 so normal rounding --> round to closest increment using two significant figures --> 1.24
• 1.23 --> this is half-way between increments 1.22 and 1.24 so ISO rounding --> 3 is odd so round up to next increment using two significant figures --> 1.24

Increment of 5

When the increment is 5, the last significant figure needs to be a digit of 0 or 5.

Examples of when the increment is 2 and rounding to two significant figures:

• 1.25 --> this already at an increment --> 1.25
• 1.252 --> this is not half-way between increments 1.25 and 1.30 so normal rounding --> round to closest increment using two significant figures --> 1.25
• 1.255 --> this is half-way between increments 1.25 and 1.30 so ISO rounding --> 5 is odd so round up to next increment using two significant figures --> 1.30
• 1.265 --> this is half-way between increments 1.25 and 1.30 so ISO rounding --> 6 is even so round down to previous increment using two significant figures --> 1.25

Applying ISO Rounding

The odd or even comparison is determined on the last significant figure which is the digit before the last digit (based on the increment), and not on the last digit as this MUST always be 5, 50, or 500, etc.

Therefore, where ISO rounding is applied, then:

• If the digit at the last significant figure is odd, then the last significant figure is rounded up to the next higher increment.
• If the digit at the last significant figure is even, then the last significant figure is rounded down to the next lower increment (unless it is already at the next lower increment).

Examples:

• If the picture is ##.# and increment is 1, and the values to round are 13.5 and 14.5, then it is the 3 and the 4, respectively, that are checked for being odd or even.
• If the picture is ##.## and increment is 10, and the values to round are 12.35 and 12.45, then it is the 3 and the 4, respectively, that are checked for being odd or even.
• If the picture is #### and the increment is 10, and the values are 1235 and 1245, then it is the 3 and the 4, respectively, that are checked for being odd or even.
• If the picture is ##### and the increment is 100, and the values are 11350 and 11450, then it is the 3 and the 4, respectively, that are checked for being odd or even.

ASTM/ISO Standard for Rounding

Refer to ASTM E29-2013 "Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications". This standard can be purchased as a download or print copy from ASTM (http://www.astm.org ). Section 6.4.4 of E29 briefly summarises what CCLAS terms as ISO rounding, that is, rounding which goes beyond the 5/4 rule:

This rounding procedure may be restated simply as follows: When rounding a number to one having a specified number of significant digits, choose that which is nearest. If two choices are possible, as when the digits dropped are exactly a 5 or a 5 followed only by zeros, choose that ending in an even digit. Table 1 gives examples of applying this rounding procedure

Note: CCLAS does not support the whole E29 standard.

In CCLAS, this rounding is performed as follows:

• When the digit beyond the one you want to keep is less than 5, do not change the digit you are keeping.
• When the digit beyond the one you want to keep is greater than 5, increase the digit you are keeping by 1.
• When the digit beyond the one you want to keep is equal to 5 and there are non-zero digits beyond it, increase the digit you are keeping by 1.
• When the digit beyond the one you want to keep is equal to 5 exactly, and the digit you are keeping is odd, increase the digit you are keeping by 1. If the digit you are keeping is even, keep it unchanged.