Question

Choose the correct relation between 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 B $2.5\times {10}^6<25,000,000$

Step 1:
Write the given numbers in scientific notation.

• $2.5\times {10}^6$ is already in scientific notation.
• $25,000,000.0$ can be written in scientific notation by moving the decimal point $7$ places to the left. And, we get the exponent to the base $10$ as $7$. Hence, $25,000,000=2.5\times {10}^7$

Step 2:
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, option (b.) is the correct one.