Write the number 5, point, 4, times, 10, to the power minus 65.4×10

Question

−6
in standard form.

Answer 1

To write the number $5.4\times {10}^{-65.4\times {10}^{-6}}$ in standard form, we start by first simplifying the exponent $-65.4\times {10}^{-6}$.

Calculating $-65.4\times {10}^{-6}$ results in: $$-0.0000654$$

Thus, the expression can now be rewritten in standard form as: $$5.4\times {10}^{-0.0000654}$$

Now, using the definition of standard form in decimal notation, we have:

$$5.4\times {10}^{-0.0000654}\text{ is essentially }5.4\times {10}^0\text{ (approximately 1)}$$

Thus, the number can be represented approximately as:

$$5.4$$

If you wanted the exact form, we would say it as $5.4\times {10}^{-0.0000654}$, which is already stated.

In conclusion, the standard form of $5.4\times {10}^{-65.4\times {10}^{-6}}$ is approximately:

$$5.4$$

However, due to the exponent being remarkably small, for practical purposes it remains $5.4\times {10}^0$ and doesn't need further adjustment.