How does the binary number system help us in everyday business?

In terms of day to day business, the binary number system holds no real advantage in the business world over decimal.

The binary number system is merely another means of representing numbers; akin to another language if you will. You can do the same operations in base 2 (binary) as base 10 (regular decimal) without losing any precision or inserting any errors. The advantage of base 10 is that people are taught to think on base 10. Everybody knows 2 + 2 = 4. Few know 0b10 + 0b10 = 0b100. (Note the use of the 0b prefix to signify binary.)

Where base 2 really holds it's own is in digital computing systems. In a digital system a data line is either on or off, 1 or 0. You cannot represent a base 10 digit on a single dateline. To directly represent a base 10 number digitally you need four datelines per digit. (This is known as Binary Coded Decimal.) However, this method is wasteful as 4 binary digits can store 0-15 but is only being used for 0-10. Also, because of that discontinuity special circuitry is required. With binary, the full range of the data bus (2 ^ (number of lines (bits)) can be utilized. Half-adders can be used for adding, and the twos-compliment method for storing negative numbers can be used which allows for subtraction using half-adders. Binary allows digital systems to operate. This, however, is unseen to most business people as knowledge of exactly how a calculator works is not requisite to use one.

I'll sum up with an old joke: There are 10 kinds of people in the world: Those who understand binary and those who don't.