Write the following numbers in the expanded form: 120719
.
Answer
362.7k+ views
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;
\[\begin{align}
& \underrightarrow{\text{Value of digit decreaes}} \\
& \underset{\underset{\begin{smallmatrix}
\text{ Hundred} \\
Thousand
\end{smallmatrix}}{\mathop{\downarrow }}\,}{\mathop{}}\,\overset{\overset{\begin{smallmatrix}
\text{ }Ten \\
Thousand
\end{smallmatrix}}{\mathop{\uparrow }}\,}{\mathop{}}\,\underset{\underset{Thousand}{\mathop{\downarrow }}\,}{\mathop{}}\,\overset{\overset{Hundred}{\mathop{\uparrow }}\,}{\mathop{}}\,\underset{\underset{\text{ Tens }}{\mathop{\downarrow }}\,}{\mathop{}}\,\overset{\overset{Unit}{\mathop{\uparrow }}\,}{\mathop{}}\, \\
& \underleftarrow{\text{Value of digits increase}} \\
& \therefore \text{ Expanded form }=100000+20000+0+700+10+9 \\
& =120719 \\
\end{align}\]
Last updated date: 29th Sep 2023
•
Total views: 362.7k
•
Views today: 6.62k
Recently Updated Pages
What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

The poet says Beauty is heard in Can you hear beauty class 6 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is the past tense of read class 10 english CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
