Question

Write the expanded form:
A) 67586412
B) 1234800007

Answer 1

Hint: Identify the position of the digits in each given numbers. Then, break the number with respect to its position in the number. Simplify the expression and hence we will get the number as the sum of the values of its digits, which is the expanded form.

Complete step by step solution: The expanded form of the number is the method to write the values of each digit of the number such that on the addition of those values, we get the initial number back.
There is place value corresponding to each digit which depends on the position of that digit in the given number.
Let us first write the number 67586412 in the place value table.

Crores	Ten-lakhs	Lakhs	Ten-Thousand	Thousand	Hundreds	Tens	Ones
6	7	5	8	6	4	1	2

Now, break up the number according to its position in the number.
Therefore, $67586412 = 6 \times 1,00,00,000 + 7 \times 10,00,000 + 5 \times 1,00,000 + 8 \times 10,000 + 6 \times 1,000 + 4 \times 100 + 1 \times 10 + 2 \times 1$
which can be further simplified as,
$67586412 = 6,00,00,000 + 70,00,000 + 5,00,000 + 80,000 + 6,000 + 400 + 10 + 2$
Hence, the expanded forms of 67586412 is $6,00,00,000 + 70,00,000 + 5,00,000 + 80,000 + 6,000 + 400 + 10 + 2$
Similarly, we will find the expanded form of 1234800007
On writing the digits of the number 1234800007 in the place value table, we get,

Hundred- crores	Ten - crores	Crores	Ten-lakhs	Lakhs	Ten-Thousand	Thousand	Hundreds
1	2	3	4	8	0	0	0

Now, break up the number according to its position in the number.
$
  1234800007 = 1 \times 1,00,00,00,000 + 2 \times 10,00,00,000 + 3 \times 1,00,00,000 + 4 \times 10,00,000 + \\
  8 \times 1,00,000 + 0 \times 10,000 + 0 \times 1,000 + 0 \times 100 + 0 \times 10 + 7 \times 1 \\
$
The above expression can also be written as,
$1234800007 = 1,00,00,00,000 + 20,00,00,000 + 3,00,00,000 + 40,00,000 + 8,00,000 + 0 + 0 + 0 + 0 + 7$
Thus, the expanded forms of 1234800007 is $1,00,00,00,000 + 20,00,00,000 + 3,00,00,000 + 40,00,000 + 8,00,000 + 0 + 0 + 0 + 0 + 7$

Note: As we move from left to right in a number, the value of digits decreases by a factor of 10 for each place. Also, we can write the number if its expanded form is given by simply adding the numbers.