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Question: 1 attometer is ………. Nanometre (A) \[{10^{ - 9}}\] (B) \[{10^{ - 8}}\] (C) \[{10^{ - 7}}\] (D...

1 attometer is ………. Nanometre
(A) 10−9{10^{ - 9}}
(B) 10−8{10^{ - 8}}
(C) 10−7{10^{ - 7}}
(D) 109{10^9}

Explanation

Solution

1 attometre is equal to 1×10−181 \times {10^{ - 18}} metres. 1 nanometer is equal to 1×10−91 \times {10^{ - 9}} meters. Using the two relations, we can multiply or divide them using the unit as a guide.

Complete Step-by-Step solution:
By the phrasal of the question, we are to find the equivalent of 1 attometre (a unit of length) in nanometre. To do this, we can use the knowledge of their conversion to metres. What is meant by this is to use the knowledge of the equivalent of attometre to metre, and the equivalent of 1 nanometre to metres.
1 attometre is equal to 1×10−181 \times {10^{ - 18}} metres i.e. 1am=10−18m1am = {10^{ - 18}}m and this also implies that 1018{10^{18}} attometre makes 1 metre that is 1018am=1m{10^{18}}am = 1m. This can be written as 1018amm{10^{18}}\dfrac{{am}}{m}
1 nanometre is equal to 1×10−91 \times {10^{ - 9}} metres i.e. 1nm=10−9m1nm = {10^{ - 9}}m and this can be written as 10−9mnm{10^{ - 9}}\dfrac{m}{{nm}}
Hence to find the equivalent of attometre in nanometre, we shall do as follows
10−9mnm×1018amm{10^{ - 9}}\dfrac{m}{{nm}} \times {10^{18}}\dfrac{{am}}{m}
Hence, by computation and cancellation of mm, we have
109amnm{10^9}\dfrac{{am}}{{nm}}
Then this means that 109{10^9} is equal to 1 nm.
Thus, by inverting 109amnm{10^9}\dfrac{{am}}{{nm}}, we have
1109nmam\dfrac{1}{{{{10}^9}}}\dfrac{{nm}}{{am}} which is equivalent to 10−9amnm{10^{ - 9}}\dfrac{{am}}{{nm}}. This implies that the 10−9{10^{ - 9}} nanometre makes 1 attometer

Hence, the correct option is A.

Note: Alternatively, we could reason as follows, if
10−18{10^{ - 18}} am is 1 m, then 10−9{10^{ - 9}} m would be equal to
10−910−18\dfrac{{{{10}^{ - 9}}}}{{{{10}^{ - 18}}}} am, and this is equal to 109{10^9}am.
Now, but 10−9{10^{ - 9}} m is 1 nm. Then 109{10^9} am is actually equal to 1 nm.
Then 1 am is equal 1109\dfrac{1}{{{{10}^9}}}am. And this is equal to 10−9{10^{ - 9}}nm.
Then 1 attometre is, indeed, equal to 10−9{10^{ - 9}}nm, which is identical to as calculated in step by step solution.