Final answer:
Multiplying by 10, 100, or 1000 is quick because it simply involves moving the decimal point without actual multiplication. Scientific notation makes this process even easier by multiplying bases and adding exponents for powers of ten. The metric system capitalizes on this ease with powers of ten for straightforward unit conversions.
Step-by-step explanation:
Multiplying by 10, 100, or 1000 is fast and easy to calculate because these are powers of ten. When multiplying by a power of ten, you don't actually multiply in the traditional sense; instead, you simply move the decimal point to the right by as many places as there are zeros in the power of ten. For example, if you multiply 4.57 by 100 (which is 10²), you move the decimal point two places to the right to get 457.
In scientific notation, this process is even more streamlined. When you multiply numbers in scientific notation, you multiply the base numbers and add the exponents of the powers of ten if there are no numbers in front. If there are numbers in front, you would multiply those first. For instance, (3 × 10⁵) × (2 × 10⁰) would become 6 × 10⁵ because 3 × 2 equals 6, and 5 + 0 equals 5 for the exponents.
The simplicity of multiplication and division by powers of ten is fundamental to the metric system, which uses these powers for easy conversion between units. This system relies on ratios that are numerically equal to 1 for each power of ten difference, hence simplifying calculations significantly.