Question

1 decimetre is _ _ _ _ megametre.
$\text{A}\text{. 1}{{\text{0}}^{-7}}$
$\text{B}\text{. 1}{{\text{0}}^{-6}}$
$\text{C}\text{. 1}{{\text{0}}^{-5}}$
$\text{D}\text{. 1}{{\text{0}}^{-8}}$

Answer 1

Hint: The values of 1 decimetre and 1 megametre in terms of a common unit. For example metre. Once you find both the values in metres, then you divide or cross multiply both the equations and find the value of 1 decimetre in terms of megametre.

Complete step by step answer:
Deci and mega are some of the prefixes used in front of the physical quantities.
Deci is most commonly used for meters. The value of deci is 0.1. The prefix deci is used when the value of the length is less than one meter. One decimetre is equal to the one tenth of a metre.
i.e. 1 decimetre = 0.1 metre ………………... (i).
When the value of the length is very large, we sometimes write the value of the length is mega metres. The value of mega is equal to one million (i.e. ${{10}^{6}}$). Therefore, one megameter is equal to one million times a metre.
i.e. 1 megameter = ${{10}^{6}}$metre …………..……. (ii).
From equation (ii) we get,
1 metre = ${{10}^{-6}}$megametre
Substitute this value of one metre in equation (i).
Therefore,
1 decimetre = $0.1\times {{10}^{-6}}$megametre.
This implies,
1 decimetre = ${{10}^{-7}}$megametre.
Hence, the correct option is A.
Additional Information: Some of the other prefixes are micro, nano and pico. These prefixes are used for the values that are very small.
The prefix nano is denoted as n. The value of nano is equal to ${{10}^{-9}}$.
The prefix micro is denoted as $\mu $. The value of micro is equal to ${{10}^{-6}}$.
The prefix pico is denoted as p. The value of pico is equal to ${{10}^{-12}}$.

Note: It is important to note that these prefixes ( deci, mega, micro, nano and pico) are just numbers and not some units. These prefixes help us to write a big digit number in short form. For example, consider the value of a length 0.000000005 metre. This can be written as 5nm.