Question

How do you write $54,000$ in standard notation?

Answer 1

Hint:
Here we need to convert it in the form where we have the power of ten multiplied by any number in which decimal is there just after the first digit. Hence we need to convert it into that form. We need to convert $54000$ into $5.4$ and accordingly multiply this by the power of $10$.

Complete step by step solution:
Here we are given to write $54,000$ in standard notation and therefore we must know what the meaning of standard notation is. Standard notation of the numbers actually means that we need to write any number that is given in the form of power of ten multiplied by any number in which decimal is there just after the first digit. This can be made clear with one example.
For example: If we need to write $2000$ in the standard notation then we need to put the decimal after the first digit and multiply that with the power of $10$ accordingly. So we need to write it in the form:
Standard notation$ = $$2.0 \times {10^n}$ where we need to calculate the value of $n$
As we have moved from the right towards left by $3$ digits. So we need to insert the power of ten as $3$
So we will get $2.0 \times {10^3}$
Similarly we are given the number $54,000$ so we need to insert the decimal after the first digit and write it in the form $5.4 \times {10^n}$ where we need to calculate the value of $n$
As we have moved from the right towards left by $4$ digits. So we need to insert the power of ten as $4$

So we will get $5.4 \times {10^4}$

Note:
Similarly if we were given to write the number which is $0.0016$ then we would have written the power of $10$ as negative as we need to insert the decimal after the original decimal and write it as $1.6 \times {10^{ - 3}}$