# Write the following numbers in the expanded form: 120719

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Last updated date: 18th Mar 2023

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Answer

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Hint: Break up the number according to their place value. The value of digits in a number increases as we move from left to right.

“Complete step-by-step answer:”

Expanded form is not the same as expanded notation. In the expanded form, we break up a number according to their place value and expand it to show the value of each digit.

Each number has a place value. It determines the value of that digit according to its position in the number. The value of a digit in a number increases as we move from left to right. The digits on the left have lower place value than the digits on the right;

\[\begin{align}

& \overset{\overset{Lakh}{\mathop{\uparrow }}\,}{\mathop{}}\,\underset{\underset{\begin{smallmatrix}

\text{ }Ten \\

Thousand

\end{smallmatrix}}{\mathop{\downarrow }}\,}{\mathop{}}\,\overset{\overset{Thousand}{\mathop{\uparrow }}\,}{\mathop{}}\,\underset{\underset{\text{ Hundred }}{\mathop{\downarrow }}\,}{\mathop{}}\,\overset{\overset{Tens}{\mathop{\uparrow }}\,}{\mathop{}}\,\underset{\underset{\text{ Ones }}{\mathop{\downarrow }}\,}{\mathop{}}\, \\

& \underleftarrow{\text{Value of digits increase}} \\

& \therefore 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) \\

& =1\times {{10}^{5}}+2\times {{10}^{4}}+0\times {{10}^{3}}+7\times {{10}^{2}}+1\times {{10}^{1}}+9\times {{10}^{0}} \\

\end{align}\]

Note: The 120719 can be also said as;

\[\begin{align}

& \underrightarrow{\text{Value of digit decreaes}} \\

& \underset{\underset{\begin{smallmatrix}

\text{ Hundred} \\

Thousand

\end{smallmatrix}}{\mathop{\downarrow }}\,}{\mathop{}}\,\overset{\overset{\begin{smallmatrix}

\text{ }Ten \\

Thousand

\end{smallmatrix}}{\mathop{\uparrow }}\,}{\mathop{}}\,\underset{\underset{Thousand}{\mathop{\downarrow }}\,}{\mathop{}}\,\overset{\overset{Hundred}{\mathop{\uparrow }}\,}{\mathop{}}\,\underset{\underset{\text{ Tens }}{\mathop{\downarrow }}\,}{\mathop{}}\,\overset{\overset{Unit}{\mathop{\uparrow }}\,}{\mathop{}}\, \\

& \underleftarrow{\text{Value of digits increase}} \\

& \therefore \text{ Expanded form }=100000+20000+0+700+10+9 \\

& =120719 \\

\end{align}\]

“Complete step-by-step answer:”

Expanded form is not the same as expanded notation. In the expanded form, we break up a number according to their place value and expand it to show the value of each digit.

Each number has a place value. It determines the value of that digit according to its position in the number. The value of a digit in a number increases as we move from left to right. The digits on the left have lower place value than the digits on the right;

\[\begin{align}

& \overset{\overset{Lakh}{\mathop{\uparrow }}\,}{\mathop{}}\,\underset{\underset{\begin{smallmatrix}

\text{ }Ten \\

Thousand

\end{smallmatrix}}{\mathop{\downarrow }}\,}{\mathop{}}\,\overset{\overset{Thousand}{\mathop{\uparrow }}\,}{\mathop{}}\,\underset{\underset{\text{ Hundred }}{\mathop{\downarrow }}\,}{\mathop{}}\,\overset{\overset{Tens}{\mathop{\uparrow }}\,}{\mathop{}}\,\underset{\underset{\text{ Ones }}{\mathop{\downarrow }}\,}{\mathop{}}\, \\

& \underleftarrow{\text{Value of digits increase}} \\

& \therefore 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) \\

& =1\times {{10}^{5}}+2\times {{10}^{4}}+0\times {{10}^{3}}+7\times {{10}^{2}}+1\times {{10}^{1}}+9\times {{10}^{0}} \\

\end{align}\]

Note: The 120719 can be also said as;

\[\begin{align}

& \underrightarrow{\text{Value of digit decreaes}} \\

& \underset{\underset{\begin{smallmatrix}

\text{ Hundred} \\

Thousand

\end{smallmatrix}}{\mathop{\downarrow }}\,}{\mathop{}}\,\overset{\overset{\begin{smallmatrix}

\text{ }Ten \\

Thousand

\end{smallmatrix}}{\mathop{\uparrow }}\,}{\mathop{}}\,\underset{\underset{Thousand}{\mathop{\downarrow }}\,}{\mathop{}}\,\overset{\overset{Hundred}{\mathop{\uparrow }}\,}{\mathop{}}\,\underset{\underset{\text{ Tens }}{\mathop{\downarrow }}\,}{\mathop{}}\,\overset{\overset{Unit}{\mathop{\uparrow }}\,}{\mathop{}}\, \\

& \underleftarrow{\text{Value of digits increase}} \\

& \therefore \text{ Expanded form }=100000+20000+0+700+10+9 \\

& =120719 \\

\end{align}\]

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