You can divide an inch in two different ways. One common way is to divide by half, then by quarters, then by eighths and so on until you divide an inch into 128 parts. This is called the fractional system. This led to complications in determining sizes. For example, which drill bit has a larger diameter: 21/64 or 53/128? Enter the decimal system. An inch is divided into a thousand parts, and a drill bit is sized to how many parts its diameter is. At a glance, you can tell that a .826 drill bit is bigger than a .573.
When using the decimal system, always refer to the size as "thousandths of an inch." For example, a drill bit size of .624 is stated as "six hundred and twenty four thousandths of an inch." Even though you know that .624 can be reduced down to 78/125, machinists and craftspeople don't do that. In the decimal system, sizes are always left in their pure decimal form, even if the number can be reduced. This applies to all machining processes, and not just drill bit sizes.
Some fractional drill bits are equivalent in size to decimal drill bits. Many decimal drill bit sizes are carried out to four places after the decimal point, to reflect that it's converted from a fraction. Suppose you have a drill bit with 7/64 stamped on it. If you divide 7 by 64, the result is .1094. As a public service, the "Math is Fun" organization provides a chart that converts fractions to decimals. The chart itself carries out the decimal to six places, but drill bit sizes are generally sized up to four places maximum.
Now that you know what the decimal system means, and how drills are sized, you may wonder about the relative sizes, or how big a drill actually is. To put the decimal system into perspective, a sheet of paper is about two thousandths of an inch thick. If you divide 1 by 4, the result is .25. Therefore, a 1/4 inch drill bit is .250, or two hundred and fifty thousandths of an inch big. Play around with a calculator and fractions to see what fractions convert to what decimals. For instance, a 3/8 inch drill bit converts to .375.