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(A) \[384000\]

(B) \[384 \times {10^3}\]

(C) \[3.84 \times {10^6}\]

(D) \[3840 \times {10^2}\]

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\[{10^3} = 1000\], so \[4 \times {10^3} = 4000\]. So \[4000\] can be written as \[4 \times {10^3}\] . This idea can be used to write even larger numbers down easily in scientific notation.

The rules when writing a number in scientific notation is that first you write down a number between \[1\] and \[10\], then you multiply it by \[10\] to the power of a number.

Scientific notation =\[m \times {10^n}\] where, \[1 \leqslant m < 10\].

The given number is \[1200 \times 3200\].We need to write the number in scientific notation.

We know that, if we need to write one number in scientific notation then we first need to write a number between \[1\] and \[10\] then multiply it by \[10\] to the power of a number.

Thus, \[1200 \times 3200 = 3840000\]

So, for expressing \[3840000\] in the scientific notation we first need to write a number between \[1\] and \[10\] then multiply it by \[10\] to the power of a number.

That is, we can express \[3840000\] as \[3.84\] multiplied by \[10\] to the power \[6\].

\[ \Rightarrow 3840000 = 3.84 \times {10^6}\]

Therefore we get,

Scientific notation of \[1200 \times 3200\] is \[3.84 \times {10^6}\].

Small numbers can also be written in scientific notation. However, instead of the index being positive (in the above example, the index was \[3\]), it will be negative. The rules when writing a number in scientific notation is that first you write down a number between \[1\] and \[10\], then you multiply it by \[10\] to the power of a number.