# The Consequences Of Rounding Errors

When you think about rounding numbers, you tend to imagine that they are natural and part of how things are. The truth is that one penny here or there, won’t make any difference at the end of the day. However, the truth is that while rounding numbers does make our lives easier, it also has some huge disadvantages.

Discover everything you need to know about rounding numbers.

While it is natural to only looking at where you usually round numbers and see that it doesn’t truly affect you, we can’t say the same thing for many other roundings that need to be made. The truth is that when you go to the grocery store or to the supermarket, you round numbers to make it easier to do the math and know how much you’ll be paying. It’s simple, easy, and really effective. However, in some roundings in some industries, the tiniest rounding can have a huge impact. These may include areas such as spaceflight, political elections, missile defense, among others.

## The Consequences Of Rounding Errors

Just to give you a simple example, in late February 1991 during the Gulf War, an Iraqi Scud missile hit American barracks in Dhahran, Saudi Arabia, killing 28 soldiers and wounding 260. This one missile accounted for more than one-third of all U.S. fatalities during the war. Although the U.S. military had deployed a Patriot defense system, it failed to fire and let the Scud through.

Take a look at Excel formula errors when you are rounding numbers.

The basic problem was in quantizing the factor used to convert the timing variable of an internal clock (represented as an integer, in tenths of a second). When a tenth of a second is represented in binary numbers, it is repeating (like 1/6 is repeating in decimal as 0.16666… with the sixes going on forever), specifically it is 0.00011001100110011 and so on, with the 0011 occurring over and over. When this is truncated to 24 bits – that is, the number of places that can be used in the representation – there is an error of 0.000000095.

This seems like an incredibly small number and it really is. Every time except when you are trying to lock onto a moving object in the sky. The Patriot tracking algorithm estimated the position of the target using this slightly-off timing variable and the velocity of the incoming missile. The end result was an error of 573 meters. The Patriot system thought the Scud was far from the barracks and did not fire.

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As we mentioned earlier, the consequences of rounding numbers can affect many different things just like they did back in the April 1992 elections in Germany. According to the German legislation, parties must surpass a minimum 5-percent threshold in order to receive seats in the legislature.

During this election in a region, one party got exactly 5% of the votes. After the election results were already published, however, someone discovered that the party had received only 4.97 percent of the vote. Nevertheless, the software they were using at the time printed out the percentages using round(), which bumped the count up to 5 percent, rather than truncating with floor(), which would have been in line with the rule.

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The reality is that the software had been used for years and no one had previously noticed, though it’s unclear whether that would have made a difference in earlier elections. After the correction, the 4.97 percent of votes corresponding to the party were thrown out according to the rule, the allocation of seats was recalculated, and the opposite party received one more spot, thereby gaining a one-seat majority.