Rounding of numbers on the Billing Report
Summary
Consider a Billing Report that is based on a Billing Model of 14.25 cents per 65 character line. If there are 20 reports eligible to bill with the following:
Characters

Lines

Rate

Amount

Rounded

4,041

62.1692308

0.01425

0.88591154

0.89

3,856

59.3230769

0.01425

0.84535385

0.85

4,709

72.4461538

0.01425

1.03235769

1.03

4,112

63.2615385

0.01425

0.90147692

0.9

3,617

55.6461538

0.01425

0.79295769

0.79

4,038

62.1230769

0.01425

0.88525385

0.89

3,851

59.2461538

0.01425

0.84425769

0.84

4,702

72.3384615

0.01425

1.03082308

1.03

4,112

63.2615385

0.01425

0.90147692

0.9

3,622

55.7230769

0.01425

0.79405385

0.79

4,041

62.1692308

0.01425

0.88591154

0.89

3,856

59.3230769

0.01425

0.84535385

0.85

4,709

72.4461538

0.01425

1.03235769

1.03

4,112

63.2615385

0.01425

0.90147692

0.9

3,617

55.6461538

0.01425

0.79295769

0.79

4,038

62.1230769

0.01425

0.88525385

0.89

3,851

59.2461538

0.01425

0.84425769

0.84

4,703

72.3538462

0.01425

1.03104231

1.03

4,112

63.2615385

0.01425

0.90147692

0.9

3,621

55.7076923

0.01425

0.79383462

0.79







1251.07692


17.8278462

$ 17.82



Rounded:

$ 17.83


In billing, we need dollars and cents. By definition, cents go two places to the right of the decimal point. For accuracy, the Billing Report carries much more precision than that.
If we carry those decimals of precision and add them all up, we get the 17.8278462. Then, if we round that to the nearest dollar, it becomes $17.83. However, if we round each job to the nearest penny then added up those rounded amounts, we get $17.82. In a list of 500 or 5,000 jobs, this rounding difference can become more prominent. It is rarely material, but it can be troubling to someone trying to tie the math to the penny.
How you handle the rounding should probably depend on how you invoice. For example, if you generate an invoice with the total number of lines, the line rate and an amount, you’ll want that math to be “correct”. In the above example, you would invoice 1251.1 lines @ .1425 = 17.8278. That rounds to 17.83. If on the other hand, you were to list each job rounded to the nearest penny, those rounded amounts will sum to $17.82.
Neither is wrong. This is just an artifact of dealing with fractional lines or rates and a monetary system that requires rounding. 