Question

Which is the correct relation for the numbers $3.28\times {10}^7$ and $4.59\times {10}^5,$ written in scientific notation?

• A. $4.59\times {10}^5>3.28\times {10}^7$
• B. $4.59\times {10}^5<3.28\times {10}^7$
• C. $4.59\times {10}^5=3.28\times {10}^7$
• D. Cannot be determined

Answer 1

The correct option is B $4.59\times {10}^5<3.28\times {10}^7$

$\underset{–}{\text{First Method:}}$

Step 1:
Write the numbers in scientific notation. Here, $3.28\times {10}^7$ and $4.59\times {10}^5$ are already in scientific notation.

Step 2:
Compare the exponents of numbers. The larger the exponent, the greater the number.
$\because 7>5$
$\Rightarrow 3.28\times {10}^7>4.59\times {10}^5$

$\underset{–}{\text{Second Method:}}$

We can compare the numbers by making the same exponent to the base $10$.

In $4.59\times {10}^5$, to convert the exponent of $10$ as $7$, we need to multiply ${10}^2$ with ${10}^5$. And, we can achieve that by moving the decimal point in $004.59$ by $2$ units to the left.

Making the powers of $10$ as $7$ for both the numbers:
$3.28\times {10}^7$ and $4.59\times {10}^5=0.0459\times {10}^7$

The number with the larger coefficient is greater.

$\because 3.28>0.0459$
$\Rightarrow 3.28\times {10}^7>0.0459\times {10}^7$

Hence, the correct comparsion between the numbers $3.28\times {10}^7$ and $4.59\times {10}^5$ would be $\underset{–}{4.59\times {10}^5<3.28\times {10}^7}$.

Therefore, option (b.) is the correct one.