## Numbers Through 1,000

In the base-ten positional numeration system, the digit farthest to the right is in the ones place. Moving to the left, each digit has a place value that is 10 times that of the digit to its right. This can be shown in a place-value chart.

Thousands Hundreds Tens Ones
10 groups of 100
or
1,000
10 groups of 10
or
100
1 group of 10
or
10
1

1

There are three basic ways of showing a number. For the number 389, these are as follows.

Standard Form
Expanded Form
Word Form
389
300 × 80 × 9
three hundred eighty-nine

When writing numbers in word form, notice that hyphens are used for numbers between 21 and 99, except for those ending in 0.

The expanded form of a number makes it clear that the value of a digit depends on its place in the numeral.

389 → 300 + 80 + 9 → (3 × 100) + (8 × 10) + 9

Comparing Greater Numbers
In this chapter, children extend comparisons to three-digit numbers. To compare 184 and 98, children will note that the first number has three digits and the second number has two digits. They will conclude that 184 > 98. This method is justified by the fact that the least 2-digit number (10) is greater than the greatest 1-digit number (9); the least 3-digit number (100) is greater than the greatest 2-digit number (99); the least 4-digit number (1,000) is greater than the greatest 3-digit number (999); and so on.

To compare two whole numbers with the same number of digits, children begin by comparing digits in each place, starting at the left. The number with the greater of the different digits is the greater number. For example, to compare 345 and 354, the same digits are in the hundreds place but there are different digits in the tens place. The fact that 4 < 5 implies that 345 < 354.

Teaching Model 20.3: Identify Place Value to 1,000