# Is your utility provider company ripping you off? By Jeff Yirak, P.E., LEED AP BD+C, O+M

Do you remember what significant figures are? If not, here’s the quick refresher- they are the digits in a number that imply the precision of the value. The more significant figures in a number, the more precise the measurement. For instance, if I said an apple weighed about 4 ounces, I would be imparting that the measurement is not particularly precise; we see just one significant figure. Technically, I’m saying the apple does weigh greater than 3.5, but less than 4.5 ounces, since a weight in this range would round to 4 ounces.

But what if I said that the apple weighed 4.04243 ounces? Here we see five significant figures, which indicate a high level of precision; clearly I used a rather exacting device to measure the weight of the apple and rounded its weight to the nearest hundred-thousandth of an ounce.

While you might not care about the weight of an apple measured to fractions of an ounce, if that precision impacted your wallet, I would have your attention.

Set the apples aside. Let’s look at my most recent residential natural gas bill: Gas consumption for space and water heating at my house.

Let’s break this bill down a little bit and check their math. The meter reading indicates I consumed 110 “CCF”, which stands for “hundred cubic feet”, with the first “C” being the Roman numeral for one hundred. This is a volumetric measurement, not an energy measurement, so an energy factor (shown as BTU factor) is applied to the volume of gas consumed to calculate the energy consumed. Table 1 below shows the per-therm multipliers that dictate the consumption cost of the gas bill. Each of these multipliers is shown to six decimal places. “Placeholder” zeroes to the right of the decimal are not considered significant figures. Table 2 below shows the price-per-therm line item charges, expanded to the correct number of significant figures: Wait a minute! That total rounds to \$130.41, not \$130.42. So why is my bill \$130.42?

Inter-calculation rounding. The delivery charge and conservation program charges both rounded up to the nearest penny, while the gas cost and merger credit rounded down. This rounding took place on a line-by-line basis, rather than in the total.

Significant figures can be a slippery slope – you may have noted that all these “per-therm” calculations are reliant on the therm usage calculation, which itself is flawed, as my meter only reads to the nearest whole CCF. The rounding errors really begin here, where all subsequent calculations can only be accurate to three significant figures.

So when do you say “enough is enough” and start rounding? Or when do you demand precision and include as many significant figures as you can get? That depends on the system. Regarding my gas bill, am I going to get my penny back? Should we be throwing rotten apples at the utility as they overcharge half of their customers one cent? When multiplied times millions of households, this puts big dollars in their pockets! Unfortunately, no; each line is correct to the nearest penny, which, unless we start minting smaller currency, is as precise as our monetary system, and thus the utility’s billing system, gets. But it’s important to see how progressive rounding in a multi-part calculation propagates error. When a system requires strict precision, every calculation counts, and the more precise the input, the more accurate your end result.

How do you like them apples?