Periods are groups of three digits separated by commas when writing numbers in standard form. This is particularly helpful for larger numbers, which can be difficult to read if there is no separation. For instance, if we wanted to write the following number written in word form, we could do so with or without commas: one billion, three hundred sixty-four million, five hundred seventy-two thousand, four hundred eighty-six.
In the first representation above, we can see that the number has 4 periods. Each new set of 3 digits makes up 1 period. Without the separation, it is more difficult to read the number. Periods allow us to quickly determine the place values of various digits in the number and therefore the magnitude of the number, whether it be in the ones, thousands, millions, billions, and so on.
Each period contains 3 places, the ones, tens, and hundreds place. For example, in the number 125, the first digit, 1, is in the hundreds place, the second is in the tens place, and the third is in the ones place. This pattern continues to the next three digits, such as 125,125, where the left-most digit is in the hundred thousands place, the next one is in the ten thousands place, and the third is in the thousands place. Below is a figure breaking up the above example into its respective place values.
Sometimes, numbers are separated into periods by spaces, such as in 1 000, or even dots like in 1.000. However, this is less common, and not really recommended, since the dot can be confused with a decimal point.
Decimal periods refer to the number of digits that repeat in a decimal. We can write numbers involving both types of periods:
The line over the "46" indicates that the 46 repeats indefinitely (127,922.4646464646...). The decimal period is therefore 2, since there are two repeating digits, while the rest of the number includes the ones and thousands periods.