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Write the following numbers in the expanded form: 120719
.
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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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