The number in the “ones” place can be read exactly as it appears. The only numbers that belong in the “ones” place are all the numbers from 0 through 9 (zero, one, two, three, four, five, six, seven, eight, and nine). The number in the “tens” place only looks like the number in the “ones” place. When viewed separately, however, this number actually has a 0 after it, making the number larger than a number in the “ones” place. The numbers that belong in the “tens” place include: 10, 20, 30, 40, 50, 60, 70, 80, and 90 (ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, and ninety).
Example: Decompose the number 82. The 8 is in the “tens” place, so this part of the number can be separated and written as 80. The 2 is in the “ones” place, so this part of the number can be separated and written as 2. When writing out your answer, you would write: 82 = 80 + 2 Also note that a number written in a normal way is written in its “standard form,” but a decomposed number is written in “expanded form. " Based on the previous example, “82” is the standard form and “80 + 2” is the expanded form.
The “ones” place and “tens” place numbers work exactly as they do when you have a two digit number. The number in the “hundreds” place will look like a “ones” place number, but when viewed separately, a number in the “hundreds” place actually has two zeroes after it. The numbers that belong in the “hundreds” place position are: 100, 200, 300, 400, 500, 600, 700, 800, and 900 (one hundred, two hundred, three hundred, four hundred, five hundred, six hundred, seven hundred, eight hundred, and nine hundred).
Example: Decompose the number 394. The 3 is in the “hundreds” place, so this part of the number can be separated and written as 300. The 9 is in the “tens” place, so this part of the number can be separated and written as 90. The 4 is in the “ones” place, so this part of the number can be separated and written as 4. Your final written answer should look like: 394 = 300 + 90 + 4 When written as 394, the number is in its standard form. When written as 300 + 90 + 4, the number is in its expanded form.
A digit in any place-position can be separated out into its separate piece by substituting the numbers to the right of the digit with zeroes. This is true no matter how large the number is. Example: 5,394,128 = 5,000,000 + 300,000 + 90,000 + 4,000 + 100 + 20 + 8
The “tenths” position is used for a single digit that comes after (to the right of) the decimal point. The “hundredths” position is used when there are two digits to the right of the decimal point. The “thousandths” position is used when there are three digits to the right of the decimal point.
Note that all numbers that appear to the left of the decimal point can still be decomposed in the same manner they would be when no decimal point is present. Example: Decompose the number 431. 58 The 4 is in the “hundreds” place, so it should be separated and written as: 400 The 3 is in the “tens” place, so it should be separated and written as: 30 The 1 is in the “ones” place, so it should be separated and written as: 1 The 5 is in the “tenths” place, so it should be separated and written as: 0. 5 The 8 is in the hundredths place, so it should be separated and written as: 0. 08 The final answer can be written as: 431. 58 = 400 + 30 + 1 + 0. 5 + 0. 08
When one addend is subtracted from the original number, the second addend should be the answer you get. When both addends are added together, the original number should be the sum you calculate.
You can combine the principles learned here with those learned in the “Decomposing into Hundreds, Tens, and Ones” section when you need to decompose larger numbers, but since there are so many possible addend combinations for larger numbers as a whole, this method would be impractical to use alone when working with large numbers.
Example: Decompose the number 7 into its different addends. 7 = 0 + 7 7 = 1 + 6 7 = 2 + 5 7 = 3 + 4 7 = 4 + 3 7 = 5 + 2 7 = 6 + 1 7 = 7 + 0
Start with the original number of something. For instance, if the number is seven, you could start with seven jellybeans. Separate the pile into two different piles by pulling one jellybean to the side. Count the remaining jellybeans in the second pile and explain that the original seven have been decomposed into “one” and “six. ” Continue separating jellybeans into two different piles by gradually taking away from the original pile and adding to the second pile. Count the number of jellybeans in both piles with each move. This can be done with a number of different materials, including small candies, paper squares, colored clothespins, blocks, or buttons.
This is easiest when used for simple addition equations, but it becomes less practical when used for long equations.
Example: Decompose and solve the equation: 31 + 84 You can decompose 31 into: 30 + 1 You can decompose 84 into: 80 + 4
Example: 31 + 84 = 30 + 1 + 80 + 4 = 30 + 80 + 5 = 100 + 10 + 5
Example: 100 + 10 + 5 = 115
