Question

Subtract $1.5\times {{10}^{3}}$ from $4.8\times {{10}^{4}}$ with due regard to significant figures.
A. $4.7\times {{10}^{4}}$
B. $4.6\times {{10}^{5}}$
C. $4.6\times {{10}^{6}}$
D. $5\times {{10}^{4}}$

Answer 1

Hint: Here, we have to subtract $1.5\times {{10}^{3}}$ from $4.8\times {{10}^{4}}$. For this, we will first make the powers of 10 the same in both these numbers. To do that, we can change either ${{10}^{3}}$ to ${{10}^{4}}$ or vice versa. Here, we will change the bigger power of 10 into the smaller one, i.e. ${{10}^{4}}$ to ${{10}^{3}}$. Once that has been done, we will subtract these numbers by taking ${{10}^{3}}$ common from both the numbers. As a result, we will get the results and then we will compare the given options with it, and thus we will get the required result.

Complete step-by-step solution
Now, we have to subtract $1.5\times {{10}^{3}}$ from $4.8\times {{10}^{4}}$. But we can see that the powers of 10 are different in both the numbers. Thus, to proceed in the question, we will first make these powers of 10 the same in both these numbers.
Now, the numbers are $1.5\times {{10}^{3}}$ and $4.8\times {{10}^{4}}$. Thus, we can see that the powers of 10 are 3 and 4. Here, we will transform the bigger power into the smaller one.
Thus, we have the number:
$4.8\times {{10}^{4}}$
Now, we know we can write it as:
$4.8\times 10\times {{10}^{3}}$
Thus, this number becomes:
$48\times {{10}^{3}}$
Now, since the powers of 10 in both numbers is the same, we can easily subtract them.
Now, we have to find the value of:
$48\times {{10}^{3}}-1.5\times {{10}^{3}}$
Now, taking ${{10}^{3}}$ common, we get:
$\begin{align}
  & 48\times {{10}^{3}}-1.5\times {{10}^{3}} \\
 & \Rightarrow \left( 48-1.5 \right)\times {{10}^{3}} \\
 & \Rightarrow 46.5\times {{10}^{3}} \\
\end{align}$
Now, if we convert the results into standard form, we will get:
$\begin{align}
  & 46.5\times {{10}^{3}} \\
 & \Rightarrow 4.65\times 10\times {{10}^{3}} \\
 & \therefore 4.65\times {{10}^{4}} \\
\end{align}$
Now, if we compare the options, we can see that option (A) is the most appropriate as $4.65\times {{10}^{4}}\approx 4.7\times {{10}^{4}}$.
Hence, option (A) is the required answer.

Note: We can also solve this question by the following method:
The given numbers are:
$1.5\times {{10}^{3}}$ and $4.8\times {{10}^{4}}$
 Now, writing them in the non-standard form we get the numbers as:
1500 and 48000
Hence, the resultant is:
$\begin{align}
  & 48000-1500 \\
 & \Rightarrow 46500 \\
\end{align}$
Now, writing 46500 in standard form we get:
$\begin{align}
  & 46500 \\
 & \therefore 4.65\times {{10}^{4}} \\
\end{align}$