Question

Compare the numbers $2.5\times {10}^6$ and $25,000,000$.

• A. $2.5\times {10}^6<25,000,000$
• B. $2.5\times {10}^6>25,000,000$
• C. $2.5\times {10}^6=25,000,000$
• D. Cannot be determined

Answer 1

The correct option is A $2.5\times {10}^6<25,000,000$

Let's compare the numbers in two steps.

Step 1:
We will write the given numbers in scientific notation.

• $2.5\times {10}^6$ is already in scientific notation.
• $25,000,000$ can be written in scientific notation by moving the decimal point $7$ places to the left. We get the exponent to the base $10$ as $7$. Hence, $25,000,000=2.5\times {10}^7$

Step 2:
Now, we will compare the exponents of numbers. The larger the exponent, the greater the number.
$\because 6<7$
$\Rightarrow 2.5\times {10}^6<2.5\times {10}^7$
$\Rightarrow 2.5\times {10}^6<25,000,000$

Therefore, $2.5\times {10}^6<25,000,000$