Place Value
The value of a digit as determined by its position in a number
Example:
The Texas Education Agency (TEA) requires the following be taught in all 5th grade public school classrooms:
(5.1) Number, operation, and quantitative reasoning. The student uses place value to represent whole numbers and decimals.
The student is expected to:
(A) use place value to read, write, compare, and order whole numbers through the 999,999,999,999; and
(B) use place value to read, write, compare, and order decimals through the thousandths place.
The Difference Between Place and Value:The place of a digit in a number is where it is placed in the place value chart. The value of a digit in a number is what it’s worth in the entire number.
For example, in the first number above, the
place of the digit 6 is the “hundred thousands place”. The
value of the 6 is 600,000.
In the second number above the
place of the 5 is the hundredths place and it’s
value is five hundredths – or 5 pieces out of a hundred.
In the decimal chart above, 0.05 or five hundredths would be shown by 5 individual squares being colored red. This should not be confused with 0.5 or five tenths which is five entire rows OR columns being shaded. (See below)
If you were to compare 0.5 (five tenths) and 0.50 (fifty hundredths) you would see that they are equal. 5 out of 10 rows is half of the whole, and 50 out of 100 is also half of the whole.
Required skills:
- Read whole numbers.
Read whole numbers through 999,999,999,999 – or nine hundred ninety-nine billion, nine hundred ninety-nine million, nine hundred ninety-nine thousand, nine hundred ninety-nine.
Each whole –number period of the place value chart (ones, thousands, millions, billions etc.) is separated from the others by a comma. When reading a number, read from left to right one period at a time. For example, in the number above, it is read “one million, six hundred twenty-three thousand, fifty-one”.
Write whole numbers from left to right as they are read. For example, in “one million, six hundred twenty-three thousand, fifty-one” a person should use the place value chart to be sure the digits are in the correct places.
- Compare and Order Whole Numbers
The most effective way to compare and order whole numbers is to stack the numbers on top of each other being sure to line up the decimals. (in the case where no decimal is visible, know that it always falls to the right of the ones place) After stacking the numbers begin at the left most digits and compare. As soon as the digits (above and below) are different, you know which number is bigger.
For example, to compare 121,112,010,212 and 121,122,010,212 you would stack them then compare. The digit in red is the first place value that is different thus making 121,122,010,212 the larger number.
121,112,010,212.
121,212,010,212.
Using this method, you could take any list of numbers and find the largest, smallest, and/or order them from least to greatest or greatest to least.
DECIMALS
In understanding decimals, it is vital to know that ALL decimal numbers represent part of one whole. All decimals have a fractional equivalent. Therefore, a longer number does not always mean a larger amount. For example 1 is a greater amount than 0.123456789 because 0.123456789 is part of a whole. In thinking about decimal place value, you will notice that all of the places on the decimal side match places on the whole number side EXCEPT the ones place. It is not possible to have a “oneths” place because it is impossible to cut something into one piece. As soon as something is cut (equal parts or not) it immediately becomes at least two parts.
- Read decimal numbers.
Read decimal numbers through 0.009– or nine thousandths.
When reading a number, read from left to right as if the number were a whole number then call the place of the last digit. . For example, in the second number above, 0.053, is pronounced “fifty-three thousandths”
- Write decimal numbers.
Write decimal numbers from left to right as they are read. For example, in “seven hundred sixty-four thousandths you write seven hundred sixty-four then count three places for the thousandths place. A person should use the place value chart to be sure the digits are in the correct places.
- Compare and Order Decimal Numbers
The most effective way to compare and order decimal numbers is to stack the numbers on top of each other being sure to line up the decimals. After stacking the numbers begin at the left most digits and compare. As soon as the digits (above and below) are different, you know which number is bigger.
For example, to compare 0.112 and 0.2, you would stack them then compare. The digit in red is the first place value that is different thus making 0.2 the larger number.
0.112
0.2
Using this method, you could take any list of numbers and find the largest, smallest, and/or order them from least to greatest or greatest to least.
*note this again illustrates that the longer number is not necessarily the larger number.