Decomposing Money
The basic meaning of decomposition is to 'split or break up'. The process of dividing or splitting a sum of money into many small units of money is called 'Decomposing money'. To decompose money it is very important to know the various denominations available for every currency. For example, let us say we have $100, and the amount to be paid to the shopkeeper is only $50, then we would have to pay a $50 bill. In this article, we will learn how to decompose money.
What is Decomposition of Money?
Money is a common term used to describe 'Currency'. Money is exchanged between various parties for buying goods or availing services. Many times we are supposed to render the exact amount to be paid or exchanged. To do that we need to know the denominations of a currency. Every country has its own currency. If we have to pay $2 to someone, we can pay 2 notes of $1, as $1 + $1 = $2. Similarly, if we have to pay 500 rupees, we can give 100 rs. + 200 rs + 200 rs, because that is one way to decompose Rs. 500.
How to Decompose Money?
Let us learn how to decompose money by taking a $100 bill. The concept of place values greatly help us in knowing about decomposing money. For example, let us take the number 100. We can split the number in the following ways:
$100 = $50 + $50 (or) $50 x 2
$100 = $10 + $10 + $10 + $10 + $10 + $10 + $10 + $10 + $10 + $10 (or) $10 x 10
$100 = $20 + $20 + $20 + $20 + $20 (or) $20 x 5
This is how we decompose money into smaller units.
Decomposition of Money in Real Life
Let us take a reallife example of supermarket grocery shopping. Joe goes to a supermarket and bought some items for $850 dollars and he had ten $100 bills. He hands over nine $100 bills to the shopkeeper and is waiting for the extra amount of money to be paid back to him. The extra amount to be returned back is $50. The shopkeeper returns him five $10 bills. Here are some more examples of decomposing various amounts of money.
$1200 = $100 x 12
$1850 = ($100 x10) + ($100 x 8) + ($50 x 1)
Purpose of Decomposition of Money
Learning how to deal with money is one of the important life skills. Many basic concepts like counting numbers, knowing place values greatly help us in dealing with the decomposition of money. Starting from a very small purchase to investing lump sums of money in a bank account, the concept of decomposition of money is very essential. The skill of decomposing money helps to manage money better. Whenever we make an investment, we deposit a certain sum of money in a bank. For example, we may have an amount of $5000, and we would like to invest only a sum of $3500. In such cases, it is very important to know how money should be decomposed or split up and what part of the money should be deposited. Similarly, decomposing money also helps us to manage our finances better by keeping a track of how much money was spent and how much money is left.
Topics Related to Decomposing Money
Here are some topics related to decomposing money.
 Money
 Money Concepts
 Adding Money Calculator
 Identifying Denominations
 Currency Converter Calculator
Solved Examples on Decomposing Money

Example 1: Decompose the following amounts of money.
a) $25 b) $45
Solution:
a) $25
$25 can be decomposed as 25 x $1 (25 one dollars)
(or) 5 x $5 (5 five dollars)
(or) 2 x $10 + 1 x $5 (2 ten dollars and one 5 dollars)b) $45
$45 can be decomposed as 45 x $1 (45 one dollars)
(or) 9 x $5 (5 five dollars)
(or) 4 x $10 + 1 x $5 (4 ten dollars and one 5 dollars)
Please note that there are various other ways also to decompose the amount with other denomination of dollar bills. 
Example 2: Write the denominations of the following amounts of money using coin currency.
a) $2 b) $5Solution:
a) $2
$2 can be decomposed as 2 x $1 (2 one dollar coins)
(or) 4 x 50 ¢ (4 fifty cents coins)
(or) 8 x 25 ¢ (8 twentyfive cents coins)
b) $5$5 can be decomposed as 5 x $1 (5 one dollar coins)
(or) 10 x 50 ¢ (10 fifty cents coins)
(or) 20 x 25 ¢ (20 twenty five cents coins)Please note that there are various other ways also to decompose the amount with other denomination of coins.

Example 3: Jim went to a stationery shop and bought some items for $43.38. He had some dollar bills and coins in his wallet. Help Jim find out in what ways he can pay the amount.
Solution:
$43.38 can be paid as (4 x $10) + (3 x $1) + ( 3 x 10 ¢) + (8 x 1 ¢)(or)
(2 x $20) + (3 x $1) + ( 1 x 25 ¢) + (13 x 1 ¢)
FAQs on Decomposing Money
What is Decomposing Numbers in Math?
The term decomposing means splitting or breaking down. Decomposing numbers is to split or break a number into smaller numbers.
How to Decompose Money?
Decomposing money means when we express an amount of money in any currency as a sum of smaller denominations. For example, $10, can be expressed as a sum of two $5.
How Do You Make 1 Dollar into Cents?
1 Dollar can be decomposed as 100 cents or two fifty cents or 4 twentyfive cents.
What Part of a Dollar is a Cent?
Onehundredth part of a dollar is a cent. This means, 100 cents make up one dollar.
How Many Cents is a Dime?
A dime is equal to 10 cents. A dime can also be decomposed as 10 one cents.