Question

Which sign in the options can replace $‘‘?"$ to make the following statement true?
$5.6\times {10}^4?5,600$

• A. $<$
• B. $>$
• C. $=$
• D. Cannot be compared

Answer 1

The correct option is B $>$

Ultimately, we need to compare the given numbers, $5.6\times {10}^4$ and $5,600.$ Let's make a comparison.

Step 1:
Write the given numbers in scientific notation.

• $\underset{–}{5.6\times {10}^4}$ is already in scientific notation.
• $5,600.0$ can be written in scientific notation by moving the decimal point $3$ places to the left. And, we get the exponent to the base $10$ as $3$. Hence, $5,600.0=\underset{–}{5.6\times {10}^3}$

Step 2:
After converting both the numbers in scientific notations, we get the same coefficient as $5.6$. Now, we can compare the exponents of numbers to find which number is greater. The larger is the exponent, the greater is the number.
$\because 4>3$
$\Rightarrow 5.6\times {10}^4>5.6\times {10}^3$
$\Rightarrow \underset{–}{5.6\times {10}^4>5,600}$

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