How to Decompose Numbers
Understand the difference between "tens" and "ones.", Break apart a two digit number., Introduce the "hundreds" place., Break apart a three digit number., Apply this pattern to infinitely larger numbers., Understand how decimals work., Break apart a...
Step-by-Step Guide
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Step 1: Understand the difference between "tens" and "ones."
When you look at a number with two digits and no decimal point, the two digits represent a “tens” place and a “ones” place.
The “tens” place is on the left, and the “ones” place is on the right.
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). -
Step 2: Break apart a two digit number.
When you are given a number with two digits, the number has a “ones” place piece and a “tens” place piece.
To decompose this number, you will need to separate it into its separate pieces.
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. , When a number has three digits and no decimal point, that number has a “ones” place, “tens” place, and “hundreds” place.
The “hundreds” place is on the left side of the number.
The “tens” place is in the middle, and the “ones” place is still on the right.
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). , When you are given a number with three digits, the number has a “ones” place piece, “tens” place piece, and “hundreds” place piece.
To decompose a number of this size, you need to separate it into all three of its pieces.
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. , You can decompose larger numbers using the same principle.
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 , You can decompose decimal numbers, but every number placed past the decimal point must be decomposed into a position piece that is also written with a decimal point.
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. , When you have a number that includes digits to both the left and right of the decimal point, you must decompose it by breaking apart both sides.
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 -
Step 3: Introduce the "hundreds" place.
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Step 4: Break apart a three digit number.
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Step 5: Apply this pattern to infinitely larger numbers.
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Step 6: Understand how decimals work.
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Step 7: Break apart a decimal number.
Detailed Guide
When you look at a number with two digits and no decimal point, the two digits represent a “tens” place and a “ones” place.
The “tens” place is on the left, and the “ones” place is on the right.
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).
When you are given a number with two digits, the number has a “ones” place piece and a “tens” place piece.
To decompose this number, you will need to separate it into its separate pieces.
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. , When a number has three digits and no decimal point, that number has a “ones” place, “tens” place, and “hundreds” place.
The “hundreds” place is on the left side of the number.
The “tens” place is in the middle, and the “ones” place is still on the right.
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). , When you are given a number with three digits, the number has a “ones” place piece, “tens” place piece, and “hundreds” place piece.
To decompose a number of this size, you need to separate it into all three of its pieces.
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. , You can decompose larger numbers using the same principle.
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 , You can decompose decimal numbers, but every number placed past the decimal point must be decomposed into a position piece that is also written with a decimal point.
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. , When you have a number that includes digits to both the left and right of the decimal point, you must decompose it by breaking apart both sides.
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
About the Author
Michael Powell
Creates helpful guides on crafts to inspire and educate readers.
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