Represent μm⋅Mg in the correct SI form using an appropriate prefix. a) Mm⋅kg, b) km⋅kg, c) m⋅kg, d) μm⋅kg, e) mm⋅kg? Can somebody explain why the answer is d.
(b) 1μm-Mg * 1km/10^9μm * 1Mg/10^3kg = 10^-12 km-kg
and so on
Sure, I can explain why the answer is d) μm⋅kg.
The prefix "μ" represents micro, which corresponds to a factor of 10^(-6) in the metric system. The symbol "m" stands for meter, and "kg" represents kilogram.
Given that "μm" represents micrometers (10^(-6) meters) and "Mg" represents megagrams (10^6 grams or a metric ton), multiplying these two units gives us micrometers multiplied by megagrams.
Since we are looking for the SI form using an appropriate prefix, we need to modify megagrams to the base unit of grams. As one megagram is equal to one million grams, the correct SI form will be μm⋅kg, where "kg" represents kilograms (the base unit of mass in the metric system).
To represent μm⋅Mg in the correct SI form using an appropriate prefix, we need to understand the prefixes used in the International System of Units (SI).
The given unit μm stands for micrometer, which is equal to 1 millionth of a meter (10^-6 m). The unit Mg represents megagram, which is equal to 1 million grams (10^6 g) or 1000 kilograms (10^3 kg).
To combine these units, we need to multiply them together, so we have:
μm⋅Mg = (10^-6 m) * (10^3 kg)
Using the rules of exponentiation, we can simplify this expression:
(10^-6 m) * (10^3 kg) = 10^-6 * 10^3 * m * kg = 10^-6+3 * m * kg = 10^-3 * m * kg
Now, let's compare the simplified expression with the options given.
a) Mm⋅kg = 10^6 * m * kg (Mm represents megameter)
b) km⋅kg = 10^3 * m * kg (km represents kilometer)
c) m⋅kg = m * kg
d) μm⋅kg = 10^-3 * m * kg (μm represents micrometer)
e) mm⋅kg = 10^-6 * m * kg (mm represents millimeter)
Comparing these options with our simplified expression, we find that only option d) μm⋅kg matches our result of 10^-3 * m * kg.
Therefore, the correct answer is d) μm⋅kg.