GED Mathematical Reasoning: Place Value

  • As a definition, whole numbers include the numbers we use to count. The set of whole numbers begins with 0 and continues with 1, 2, 3, 4, and so on.
  • A whole number may contain one digit or many digits. For example, the number 4,526 is a whole number with 4 digits.
  • Each digit has value based on its place in the number.
  • Here is the place value chart for your reference:

Millions

Thousands Ones

hundred millions

ten millions

millions hundred thousands ten thousands thousands hundreds tens ones
  • Reading from right to left, the ones place comes first and is followed by the tens place, hundreds place, thousands place, and so on.
  • A comma is sometimes used to separate the thousands place from the hundreds place. Also, to separate the millions place from the hundred thousands place. For instance, the number 4,526 can be written as four comma five two six or as simply four five two six.
  • Zero is used as a placeholder to denote that a place has no value. For example, if you have $304 you might think of it in terms of place value as having 3 one-hundred dollar bills, no ten dollar bills, and 4 one-dollar bills.

math 202

 

Example 1

Which of the following whole numbers can be described as: 3 ones, 9 tens, 2 hundreds, and 7 thousands?

  1. 7,392
  2. 7,293
  3. 3,927
  4. 3,729

 

Reading from left to right, the thousands place comes first, then the hundreds place, followed by the tens place, and finally the ones place. Each digit provided within the question should be placed in this order. So we’ll first write a 7 in the thousands place, then a 2 in the hundreds place, then a 9 in the tens place, and finally a 3 in the ones place. Therefore the correct answer is (2).

 

Example 2

Which of the following numbers is greater than 210 but less than 250?

  1. 310
  2. 190
  3. 265
  4. 242

 

So in this question, we are looking for the number that falls between 210 and 250. We can use place value to make sense of and compare whole numbers. We begin with the largest place value and compare the digits of the two numbers. We will stop when we reach a place value with digits that are different.

Notice that both 210 and 250 have a 2 in the hundreds place. A number that falls between 210 and 250 will also have a 2 in the hundreds place. That eliminates answers (1) and (2) because they contain a 3 and a 1 in the hundreds place, respectively. Now look at the tens place. The number 210 contains a 1 in the tens place and the number 250 contains a 5. Therefore, a number that falls between 210 and 250 will have a number in the tens place that is between 1 and 5.

The remaining answer that meets this criterion is answer (4) 242.

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