Standard Form (Scientific Notation)

In $47,000$, the decimal point sits after the last zero: $47000.$

Move the decimal point left until one non-zero digit remains to its left: $47000.$ → $4.7000$

The decimal moved 4 places to the left, so the exponent is $+4$.

$47,000=4.7\times 10^4$. The coefficient $4.7$ satisfies $1\le 4.7<10$. ✓

The coefficient $A$ must satisfy $1\le A<10$. This eliminates $47\times 10^3$ (coefficient is 47) and $0.47\times 10^5$ (coefficient is less than 1).

We are left with $4.7\times 10^4$ and $4.7\times 10^3$.

$4.7\times 10^3=4,700$ and $4.7\times 10^4=47,000$.

$4.7\times 10^4=47,000$ matches the original number. ✓

The number $0.000063$ is less than 1, so it will have a negative exponent in standard form.

Move the decimal point right until one non-zero digit is to its left: $0.000063$ → $6.3$

The decimal moved 5 places to the right, so the exponent is $-5$.

$0.000063=6.3\times 10^{-5}$. ✓

$63\times 10^{-6}$ has coefficient 63, which is not between 1 and 10. Eliminate it.

Since $0.000063<1$, the exponent must be negative. Eliminate $6.3\times 10^5$.

We are left with $6.3\times 10^{-4}$ and $6.3\times 10^{-5}$.

$6.3\times 10^{-4}=0.00063$ and $6.3\times 10^{-5}=0.000063$. The second matches. ✓