Question

Write down the numbers whose expanded form is as below
A) $8\times{10^5} + 6\times{10^2} + 6\times{10^0}$
B) $3\times{10^4} + 6\times{10^3} + 5\times{10^2} + 8\times{10^0}$
C) $8\times{10^5} + 2\times{10^3} + 3\times{10^1}$
D) $7\times{10^6} + 6\times{10^3} + 5\times{10^1} + 3\times{10^0}$

Answer 1

Hint:
At first we need to expand the numbers given in powers of ten and multiplying with the given numbers and writing the numbers at the correct place value we get the standard form of the numbers.

Complete step by step solution:
We are given the expanded form of the numbers and asked to write it in the standard form
A) $8\times{10^5} + 6\times{10^2} + 6\times{10^0}$
Here ${10^5}$ can be written as 100000
And ${10^2}$can be written as 100
And by the property ${a^0} = 1$ we get ${10^0} = 1$
Now substituting this we get
$\
   \Rightarrow 8\times100000 + 6\times100 + 6\times1 \\
   \Rightarrow 800000 + 600 + 6 \\
 $
Here we have 8 in the lakhs place and 6 in the hundreds place and 6 in the units place
For the other place values we need to write zero
$ \Rightarrow 800606$

B) $3\times{10^4} + 6\times{10^3} + 5\times{10^2} + 8\times{10^0}$
Here ${10^4}$ can be written as 10000
And ${10^3}$ can be written as 1000
And ${10^2}$can be written as 100
And by the property ${a^0} = 1$ we get ${10^0} = 1$
Now substituting this we get
$\
   \Rightarrow 3\times10000 + 6\times1000 + 5\times100 + 8\times1 \\
   \Rightarrow 30000 + 6000 + 500 + 8 \\
 $
Here we have 3 in the ten thousand place and 6 in the thousands place and 5 in the hundreds place and 8 in the units place
For the other place values we need to write zero
$ \Rightarrow 36508$

C) Here ${10^5}$ can be written as 100000
And ${10^3}$can be written as 1000
And ${10^1}$can be written as 10
Now substituting this we get
$\
   \Rightarrow 8\times100000 + 2\times1000 + 3\times10 \\
   \Rightarrow 800000 + 2000 + 30 \\
 $
Here we have 8 in the lakhs place and 2 in the thousands place and 3 in the tens place
For the other place values we need to write zero
$ \Rightarrow 802030$

D) $7\times{10^6} + 6\times{10^3} + 5\times{10^1} + 3\times{10^0}$
Here ${10^6}$ can be written as 1000000
And ${10^3}$ can be written as 1000
And ${10^1}$can be written as 10
And by the property ${a^0} = 1$ we get ${10^0} = 1$
Now substituting this we get
$\
   \Rightarrow 7\times1000000 + 6\times1000 + 5\times10 + 3\times1 \\
   \Rightarrow 7000000 + 6000 + 50 + 3 \\
 $
Here we have 7 in the ten lakhs place and 6 in the thousands place and 5 in the tens place and 3 in the units place
For the other place values we need to write zero
$ \Rightarrow 7006053$

Note:
They can also ask the same question in a reverse way also. They’ll be giving us these numbers and will ask us to write the numbers into expanded form. for this, we’ll write each number multiplied by its place value. as it was given to us in the question.