Question

Write the following numbers in the expanded forms:
279404, 3006194, 2806196, 120719, 20068.

Answer 1

Hint: To solve the question given above, we will write the unit digit number as the product of that number and the tens place digit number as the product of that number and 10, the hundreds place digit number as the product of that number by adding ‘+’ sign between them.

Complete step-by-step answer:
Before solving the question, we will explain what expanded forms in number is. Expanded form is a way of writing numbers to see the math value of individual digits. In other words, in the expanded form, we break up a number according to their place value and expand it to show the value of each digit. In this question, we are given five numbers and we will write the expanded form separately in parts.
279404: To write this number in expanded form, we will have to represent this number as the sum of $\text{k }\times \text{ 1}{{\text{0}}^{n}}$ where $0\text{ }\le \text{ k }\le \text{ 9}$ and n is any whole number. To start with, we will write units place digit as shown:
(i) \[\begin{align}
  & \Rightarrow 4\text{ = 4 }\times \text{ 1}{{\text{0}}^{\circ }} \\
 & \Rightarrow \text{ 4 = 4 }\times \text{ 1} \\
\end{align}\]
Similarly we will write:\[0\text{ as }0\text{ }\times \text{ 10, 4 as 4 }\times \text{ 100, 9 as 9 }\times \text{ 1000, 7 as 7 }\times \text{ 10000 and 2 as 2 }\times \text{ 100000}\text{.}\]
Thus, the expanded form is:
\[\begin{align}
  & 279404\text{ = }\left( 2\times 100000 \right)+\left( 7\times 10000 \right)+\left( 9\times 1000 \right)+\left( 4\times 100 \right)+\left( 0\times 10 \right)+\left( 4\times 1 \right) \\
 & 279404\text{ = 200000 + 70000 + 9000 + 400 + 0 + 4} \\
\end{align}\]
(ii) 3006194: First we will write unit place digit as shown:
\[\begin{align}
  & \Rightarrow 4\text{ = 4 }\times \text{ 1}{{\text{0}}^{\circ }} \\
 & \Rightarrow \text{ 4 = 4 }\times \text{ 1} \\
\end{align}\]
Now, the tens place digit is represent as: \[9\times \text{10}\] Similarly hundreds place as \[1\times \text{100}\] thousands place as \[6\times \text{1000}\] and so on. Thus, the expanded form is:
\[\begin{align}
  & 3006194\text{ = }\left( 3\times 1000000 \right)+\left( 0\times 100000 \right)+\left( 0\times 10000 \right)+\left( 6\times 1000 \right)+\left( 1\times 100 \right)+\left( 9\times 10 \right)+\left( 4\times 1 \right) \\
 & 3006194\text{ = 3000000 + 0 + 0 + 6000 + 100 + 90 + 4} \\
\end{align}\]
(iii) 2806196: The units place will be represented as: \[6\times \text{1}\] The tens place will be represented as \[9\times \text{10}\] hundreds place will be represented as \[1\times \text{100}\] and so on. Thus, the expanded form:
\[\begin{align}
  & 2806196\text{ = }\left( 2\times 1000000 \right)+\left( 8\times 100000 \right)+\left( 0\times 10000 \right)+\left( 6\times 1000 \right)+\left( 1\times 100 \right)+\left( 9\times 10 \right)+\left( 6\times 1 \right) \\
 & 2806196\text{ = 2000000 + 800000 + 0 + 6000 + 100 + 90 + 6} \\
\end{align}\]
(iv) 120719: Similar to above solved parts, 120719 can be represented in the expanded form as shown below:
\[\begin{align}
  & \text{120719 = }\left( 1\times 100000 \right)+\left( 2\times 10000 \right)+\left( 0\times 1000 \right)+\left( 7\times 100 \right)+\left( 1\times 10 \right)+\left( 9\times 1 \right) \\
 & \text{120719 = 100000 + 20000 + 0 + 700 + 10 + 9} \\
\end{align}\]
(v) 20068: The expanded form of 20068 is as shown:
\[\begin{align}
  & \text{20068 = }\left( 2\times 10000 \right)+\left( 0\times 1000 \right)+\left( 0\times 100 \right)+\left( 6\times 10 \right)+\left( 8\times 1 \right) \\
 & 20068\text{ = 20000 + 0 + 0 + 60 + 8} \\
\end{align}\]

Note: If 0 is coming in between the first and the last digit of the number then also we have to write it as a product of zero and the power of 10, although it will eventually become zero. Also, we do not have to add the numbers in the answer. We just have to leave it that way.