Question

Write the corresponding numeral for the following:
\[5 \times 100000 + 8 \times 10000 + 1 \times 1000 + 6 \times 100 + 2 \times 10 + 3 \times 1\]

Answer 1

Hint: Here, we will use the modern numeral system i.e. the place-value systems to construct all the numbers. We will multiply each term separately and then substitute their values in the given expression. Adding all the terms together will give us the required value.

Complete step-by-step answer:
Given expanded form of the required numeral is:
\[5 \times 100000 + 8 \times 10000 + 1 \times 1000 + 6 \times 100 + 2 \times 10 + 3 \times 1\]
Now, we will separate each term from this expanded form from the addition sign between them.
Hence, we get:
First term \[ = 5 \times 100000 = 500000\] …………………………..\[\left( 1 \right)\]
Second term \[ = 8 \times 10000 = 80000\] ………………………….\[\left( 2 \right)\]
Third term \[ = 1 \times 1000 = 1000\] …………………….…………….\[\left( 3 \right)\]
Fourth term \[ = 6 \times 100 = 600\] …………………………………..\[\left( 4 \right)\]
Fifth term \[ = 2 \times 10 = 20\] ………………………………………….\[\left( 5 \right)\]
Sixth term \[ = 3 \times 1 = 3\] ……………………………………………...\[\left( 6 \right)\]
Now, since, each term was separated by an additional sign between them in the expanded form.
We will add \[\left( 1 \right)\], \[\left( 2 \right)\], \[\left( 3 \right)\], \[\left( 4 \right)\], \[\left( 5 \right)\] and \[\left( 6 \right)\] to get the required corresponding numeral of the given expanded form.
\[ \Rightarrow 5 \times 100000 + 8 \times 10000 + 1 \times 1000 + 6 \times 100 + 2 \times 10 + 3 \times 1 = 500000 + 80000 + 1000 + 600 + 20 + 3\]
\[ \Rightarrow 5 \times 100000 + 8 \times 10000 + 1 \times 1000 + 6 \times 100 + 2 \times 10 + 3 \times 1 = 5,81,623\]
Therefore, the required corresponding numeral of the given expanded form is 581623.
Hence, this is the required answer.

Note: In mathematics, expanded form of a number means that the specific number is represented as the sum of each digit present in that number multiplied by its place value respectively. Whereas, a numeral form of a number is the mathematical symbol or name that stands for a number. Also, in this question, we could have used the method of BODMAS which states that first of all we are required to do multiplication and then, addition. Hence, we could have directly multiplied all the numbers and then, added them together as below:
\[5 \times 100000 + 8 \times 10000 + 1 \times 1000 + 6 \times 100 + 2 \times 10 + 3 \times 1 = 500000 + 80000 + 1000 + 600 + 20 + 3\]
\[ \Rightarrow 5 \times 100000 + 8 \times 10000 + 1 \times 1000 + 6 \times 100 + 2 \times 10 + 3 \times 1 = 5,81,623\]
Therefore, the required corresponding numeral of the given expanded form is 581623.