Simpler Version:

To multiply a number by a power of ten, move the decimal point to the right by the number of places equal to the exponent of ten. For example, multiplying 5 by 10^3 would result in 5000.

To divide a number by a power of ten, move the decimal point to the left by the number of places equal to the exponent of ten. For example, dividing 5000 by 10^3 would give you 5.

Same Version:

Whether the numbers have decimals or not, the process of multiplying or dividing by powers of ten remains the same. To multiply, shift the decimal point to the right by the exponent of ten. To divide, shift the decimal point to the left by the exponent of ten.

More Complex Version:

When multiplying a number by a power of ten, you can easily achieve the desired result by shifting the decimal point to the right. The number of places you move the decimal point is determined by the exponent of ten. For instance, multiplying 5 by 10^3 requires moving the decimal point three places to the right, resulting in 5000.

Similarly, when dividing a number by a power of ten, you can accomplish this by shifting the decimal point to the left. The number of places you move the decimal point is determined by the exponent of ten. For example, dividing 5000 by 10^3 necessitates moving the decimal point three places to the left, yielding 5.

These rules apply universally, regardless of whether the numbers involved have decimals or not. By understanding these principles, you can confidently multiply and divide numbers by powers of ten, simplifying calculations and achieving accurate results.