A state department of education, as a question on the public-release form of a statewide standardized test, released a question to the public in which students have to recognize equivalent representations of whole numbers and their place values.
I’m going to use the word DIGIT to mean the numerals 0 through 9. This question gives us a number, 5,360. We are asked to determine the value of the DIGIT 6 in this number.
The value of a DIGIT in any number is based upon its location or placement in the number. That location in the number of a DIGIT is known as its “place” and the total amount that the DIGIT is worth in the number is known as its “place value,” (the VALUE it has because of its PLACE in the number).
For example, there are four DIGITS in 5,360. The 0 is said to be in the ones place, because it is furthest to the right in the number. The lowest place in a whole number is the ones place. Next is the tens place, and the 6 is in the tens place in our number. It has a place value of 60, because we multiply the number in the tens place by 10 to determine its value.
In other words, because the DIGIT 6 is in the tens place in our number, we know there are six 10’s in the number. Since 6 × 10 = 60, we know the value of the “6” in our number is 60.
That’s the answer to our question, but let’s continue.
We have a 3 in the hundreds place, which has a value of 3 × 100 = 300, and a 5 in the thousands place, with a value of 5 × 1,000 = 5,000.
We can also write the number in expanded form. This is another way to show what the number really means. The number 5,360 would look like this in expanded form:
Some teachers say it is OK to leave out the “+ 0” since it really has no value in the number. However, putting it in is definitely mathematically correct, so I figure it’s best to make sure all your bases are covered.
In addition, some teachers say it is OK to leave out the “= 5,360” when writing the number in expanded form. Different textbooks say different things about exactly what to include or leave out when writing a number in expanded form, and it is not our place to throw ourselves into the debate.
We would advise you to ask your teacher how he or she prefers to write numbers in expanded form, and as long as it’s still a mathematically correct formula or style, go ahead and use that. It’s much more important to do the problem as your teacher tells you than it is to discuss what exact form constitutes expanded form.
If you would like additional problems to help you master this skill, go to our online card catalog at VoxLearn.org, select one of the math collections, and enter the search terms “place value” or “expanded form.”