Question

Fill in the blanks in the following conversions:
(i) 1 km=⋯⋯mm=⋯⋯pm
(ii) 1 mg =⋯⋯kg=⋯⋯ng
(iii)1 mL=⋯⋯L=⋯⋯ $d{{m}^{3}}$

Answer 1

Hint: Unit conversions are often necessary to convert a value from one system of units into another unit. In the case of a scientific unit's metric system is the preferred system for several reasons such as world wide acceptance, the prefixes attached to the metric unit etc. For the conversions prefixes are used.

Complete answer:
  - The metric system is usually based on the powers of ten because after the metric unit conversions a measurement in the metric system which is represented by a rational number remains a rational number.
  - The base units used in the metric system are meter(length), gram (Mass) and liter(volume). The metric based systeme International (SI) is frequently used to standardize the calculation of several scientific quantities.
  - Prefixes are attached to base units in the metric system in order to change the scale. It represents a factor by which the base unit should be multiplied. Some examples of prefixes are Kilo(${{10}^{3}}$),milli (${{10}^{-3}}$), Pico(${{10}^{-12}}$), nano(${{10}^{-9}}$) etc.
  - We are asked to convert some of the given units. Let's take each of them and convert accordingly
(i) 1 km=⋯⋯mm=⋯⋯pm
As we mentioned above Kilo represents ${{10}^{3}}$ ,Milli represents ${{10}^{-3}}$ and Pico represents ${{10}^{-12}}$. In the question the basic unit is metre(length). From the above observations we can write as follows
1 km=${{10}^{3}}$m=${{10}^{6}}$mm
1 pm=${{10}^{-12}}$m Hence 1m=${{10}^{12}}$ pm
Thus, the answer is 1 km=${{10}^{6}}$ mm=${{10}^{15}}$ pm

(ii) 1 mg =⋯⋯kg=⋯⋯ng
Here the base unit is grams(mass). The interconversion between units are given below,
1 kg=${{10}^{3}}$g=${{10}^{6}}$mg
1 ng=${{10}^{-9}}$g; Hence 1g= ${{10}^{9}}$ ng
Thus, the answer is 1 mg =${{10}^{-6}}$ kg=${{10}^{6}}$ng

(iii)1 mL=⋯⋯L=⋯⋯ $d{{m}^{3}}$
Here the base unit is litre(volume). The conversion is given below,
1 ml=${{10}^{-3}}$L and 1 L= 1$d{{m}^{3}}$
Thus the answer is 1 mL=${{10}^{-3}}$L=${{10}^{-3}}$$d{{m}^{3}}$

Note:
It should be noted that, even though the SI Units are nearly global, countries such as the United States, Burma, and Liberia have not officially adopted the International System of Units as their primary system of measurements. Also, there are many other prefixes which we have not mentioned here such as Giga, Hecto, Deka, mega etc.