Question

The population of city $A$ is $4.81\times {10}^6$, the population of city $B$ is $1.9\times {10}^5$ , and the population of city $C$ is $7,421,000$. Arrange the cities in increasing order of their population.

Answer 1

Detailed step-by-step solution:
Representation of the population of the cities in scientific notation:

The population of city $A=4.81\times {10}^6$
The population of city $B=1.9\times {10}^5$
The population of city $C=7,421,000=7.421\times {10}^6$ (writing the number in scientific notation)
The population of $3$ cities are represented in scientific notation.

To compare the numbers written in scientific notation, we can compare their powers of $10$. The number with the greatest power of $10$ will be the greatest number. If two numbers have the same power of $10$ , then compare the decimal numbers to determine the greatest number.

$\to 1.9\times {10}^5<4.81\times {10}^6<7.421\times {10}^6$

$\to \text{City}B<\text{City}A<\text{City}C$

$\to B<A<C$

$\to$ Option B is correct.

Alternate approach:

Representation of the population of the cities in the standard form:
The population of $\text{City}A=4.81\times {10}^6=4.8100000\times 106$

Zeros are added after the factor $4.81$ as the exponent of $10$ in $4.81\times {10}^6$ is $6$ , which is a positive integer. So, the decimal point will shift to the right by 6 places.
So, $4.81\times {10}^6=4,810,\mathrm{000.0.}$

The population of city $B=1.9\times {10}^5=1.900000\times {10}^5$

The exponent of $10$ in $1.900000\times {10}^5$ is $5$, which is a positive integer. So, the decimal point will shift to the right by $5$ places.

So, $1.900000\times {10}^5=\mathrm{190000.0.}$
$\because 190,000<4,810,000<7,421,000$

$\therefore$ The cities in ascending order by their population will be $B<A<C.$

$\to$ Option B is correct.