ABE Math Tutorials/Whole numbers/Place value

From WikiEducator
Jump to: navigation, search

Place value

Tutorial.png Whole numbers 

Introduction | Place value | Rounding | Long addition & subtraction | Long Multiplication | Long division | Expressing operations | Word problems | Order of operations | "Set-up" problems | Cost and distance problems | Introduction to algebra | Powers of 10 | Estimation | Not enough info | Homework


Icon reflection.gif


Have you ever thought about what the number "14" means?

First we write down a digit "1", then we write down a digit "4". What does this mean? Does it mean "1 + 4" ? Does it mean "1 x 4" ? Of course not! We realize that the digit "1" doesn't really mean "1" at all; it really stands for "10". The number "14" means one group of 10 plus four ones.

Icon key points.gif
Key points
Words to Know
  1. digit:a "single" numeral; like 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.
  2. number:one or more digits put together; like 42, 788, 5, 332,761, etc.

Now let's consider a bigger number, like 4,971. When we say this number out loud, we can hear what the digits stand for: 4 thousand, nine hundred and seventy-one. This means: 4 thousands plus 9 hundreds plus 7 tens (the word "seventy" actually means "seven-tens") plus one. Mathematically, we say:

  • the 4 is in the thousands' place
    • the 9 is in the hundreds' place
      • the 7 is in the tens' place
        • the 1 is in the ones' place

This idea, that every digit in a number has its place, is called place value.Now, let's look at an even larger number: 6,408,554 (6 million, four-hundred-and-eight thousand, five hundred and fifty-four). To figure out what the place value is of each digit in this number, we can write it down in a table like the one below.

millions hundred thousands ten thousands thousands hundreds tens ones
6 4 0 8 5 5 4

Number 6,408,554

Notice that the last digit in a number always goes in the ones' place; the second-to-last digit always goes in the tens' place; the third-to-last digit (if there is one) always goes in the hundreds' place; and so on. Look at this number (6,408,554) once again.}}

What is the place value of the 8?: When you look at the table, you can see that the 8 is in the thousands place. What is the place value of the 6?: You can see that the 6 is in the millions place. What is the place value of the 0?:The 0 (zero) is in the ten-thousands place. This means that there are no ten-thousands in this number, but if we left out the zero, we would get an entirely different number (648,554)!

In the table below, the first three numbers on the right-hand side have been separated into their place values. Try writing out the other three numbers into the table (you can print this page off to do this; or just write out the numbers on a piece of scrap paper):

Number 3,469,114 429 70,001 7,280 23 9,879,745

millionshundred thousandsten thousandsthousandshundredstensones
Icon qmark.gif

Self Assessment

Now try answering the following questions:
  1. In the number 429; the 4 is in the _______________ place.
  2. In the number 3,469,114; the 6 is in the ________________place.
  3. In the number 70,001, which digit is in the thousands' place?
  4. In the number 9,879; which digit is in the tens' place?
  5. In the number 7,280; the 2 is in the ______________place.
  6. In the number 23, which digit is in the hundred-thousands' place?

Bold text