Paul Van de Vanter, age 11, of Utica, N.Y., for his question:

CAN YOU EXPLAIN THE DECIMAL NUMERAL SYSTEM?

The decimal numeral system is the way we express numbers. The name “decimal” comes from the Latin word for “ten.”

In this system we use single number symbols called numerals to express numbers from one to nine. Then we use two numbers to express a ten: a one and a zero. The number 10 is the base of the decimal numeral system.

The decimal numeral system is one of the world’s most useful ways of expressing numbers. It uses only 10 numerals.

You can express the numeral 14 by using a system of place value. You do not need to invent a new symbol for 14. You use two digits you already know: 1 and 4.

By counting, you can see that 14 consists of a group of 10 things and a group of four things. You can use 1 to stand for the group of 10 things and 4 to stand for the group of four things. You can see that a digit occupies a space or place on the page. Two digits together occupy two places.

You use the first place on the right for single things. You use the second place to the left for groups of 10 things. Take a look at the number 22.

Place value means that the value or the number of things for which a digit stands, depends on the place it occupies. In the first place on the right, a 2 means two 1’s. In the second place to the left, it means two 10’s. Your number is 22.

Using two places, you can write the numerals from 10 to 99. To write one hundred, you must use the third place to the left. The number 100 stands for one group of a hundred things. Because there are no 1’s or 10’s, you must write zeros in the 1’s and 10’s places.

You use the fourth place to the left for thousands, the fifth for ten thousands, the sixth for one hundred thousands and the seventh for millions.

We can also write fractions with the decimal numeral system. Six tenths is written as .6.

Take a look at the number 5,705,368. Can you name the place values?

This number means you have five millions, seven hundred thousands, no ten thousands, five thousands, three hundreds, six tens and eight ones. In writing such a number, you set off every three digits with a comma starting at the right and counting to the left. These groups of three digits set off by commas are called periods.

Here are the names of the periods we use in the decimal numeral system:

The numeral thousand is followed by three zeros and the numeral million is followed by six zeros. Billion is followed by nine zeros while trillion is followed by 12 zeros.

Quadrillion is followed by 15 zeros. Quintillion is followed by 18 zeros and sextillion is followed by 21 zeros.

Septillion is followed by 24 zeros, octillion by 27 zeros, nonillion by 30 zeros, decillion by 33 zeros, undecillion by 36 zeros and duodecillion by 39 zeros.

Tredecillion is followed by 42 zeros. quattuodecillion by 45 zeros, quindecillion by 48 zeros, sexdecillion by 51 zeros and septendecillion by 54 zeros.

Octodecillion is followed by 57 zeros, novemdecillion by 60 zeros and vigintillion by 63 zeros. There are no standard names for numbers with periods to the left of vigintillion.