Chapter 1: Our Number System 5The ancient Romans weren’t the only culture to have their own number system. There were
many, with different organizing principles. The system most commonly in use today originated
with Arabic mathematicians and makes use of a positional, or place value system. In many ancient
systems, each symbol had a fixed meaning, a set value, and you simply combined them. In a place
value system, each position represents a value and the symbol you place in that position tells how
many of that value are in the number.DEFINITION
A place value system is a number system in which the value of a symbol depends on
where it is placed in a string of symbols.The Decimal System
Our system is a positional, or place value system, based on the number 10, and so it’s called a
decimal system. Because it’s based on 10, our system uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
A single digit, like 7 or 4, tells you how many ones you have.DEFINITION
A digit is a single symbol that tells how many. It’s also a word that can refer to a finger
(another way to show how many).When you start to put together digits, the rightmost digit, in the ones place, tells you how many
ones you have, the next digit to the left is in the tens place and tells how many tens, and the next
to the left is how many hundreds. That place is called the hundreds place. The number 738 says
you have 7 hundreds, 3 tens, and 8 ones, or seven hundred thirty-eight.
The number 392,187 uses six digits, and each digit has a place value. Three is in the hundred-
thousands place, 9 in the ten-thousands place, and 2 in the thousands place. The last three digits
show a 1 in the hundreds place, 8 in the tens place and 7 in the ones place.The Meaning of Digits in a Place Value SystemPlace NameHundred-
thousandsTen-
thousands Thousands Hundreds Tens Ones
Value 100,000 10,000 1,000 100 10 1
Digit 3 9 2 1 8 7
Worth 300,000 90,000 2,000 100 80 7