Place value assigns each digit in a number system a greater or lesser value depending upon where it appears in a number. The number system used most commonly throughout the world is the Hindu-Arabic number system. This system contains ten digits (also called numerals), which are symbols like the letters A through Z:
1 2 3 4 5 6 7 8 9 0
Like letters of the alphabet, individual digits aren’t very useful. When used in combination, however, these ten symbols can build numbers as large as you like using place value. Each place in a number is ten times greater than the place to its immediate right.
Although the digit 0 adds no value to a number, it can act as a placeholder. When a 0 appears to the right of at least one non-zero digit, it’s a placeholder. Placeholders are important for giving digits their proper place value. In contrast, when a 0 isn’t to the right of any nonzero digit, it’s a leading zero. Leading zeros are unnecessary and can be removed from a number.
Sample questions
In the number 284, identify the ones digit, the tens digit, and the hundreds digit.
The ones digit is 4, the tens digit is 8, and the hundreds digit is 2.
Place the number 5,672 in a table that shows the value of each digit. Then use this table and an addition problem to show how this number breaks down digit by digit.
Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones 5 6 7 2 The numeral 5 is in the thousands place, 6 is in the hundreds place, 7 is in the tens place, and 2 is in the ones place, so here’s how the number breaks down:
5,000 + 600 + 70 + 2 = 5,673
Place the number 040,120 in a table that shows the value of each digit. Then use this table to show how this number breaks down digit by digit. Which 0s are placeholders, and which are leading zeros?
Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones 0 4 0 1 2 0 The first 0 is in the hundred-thousands place, 4 is in the ten-thousands place, the next 0 is in the thousands place, 1 is in the hundreds place, 2 is in the tens place, and the last 0 is in the ones place, so
0 + 40,000 + 0 + 100 + 20 + 0 = 40,120
The first 0 is a leading zero, and the remaining 0s are placeholders.
Practice questions
Identify the ones, tens, hundreds, and thousands digit in the number 7,359.
a. The ones digit
b. The tens digit
c. The hundreds digit
d. The thousands digit
Place the number 2,136 in a table that shows the value of each digit. Then use this table to show how this number breaks down digit by digit.
Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones
Place the number 03,809 in a table that shows the value of each digit. Then use this table to show how this number breaks down digit by digit. Which 0 is a placeholder and which is a leading zero?
Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones
Place the number 0,450,900 in a table that shows the value of each digit. Then use this table to show how this number breaks down digit by digit. Which 0s are placeholders and which are leading zeros?
Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones
The following are the answers to the practice questions:
The answers:
a. 9 is the ones digit.
b. 5 is the tens digit.
c. 3 is the hundreds digit.
d. 7 is the thousands digit.
2,000 + 100 + 30 + 6 = 2,136
Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones 2 1 3 6 0 + 3,000 + 800 + 0 + 9 = 3,809. The 0 in the ten-thousands place is the leading zero, and the second 0 is the placeholder.
Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones 0 3 8 0 9 0 + 400,000 + 50,000 + 0 + 900 + 0 + 0 = 0,450,900. The 0 in the millions place is a leading zero, and the remaining three 0s are placeholders.
Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones 0 4 5 0 9 0 0