Question

Write \[1200 \times 3200\] in scientific notation.
(A) \[384000\]
(B) \[384 \times {10^3}\]
(C) \[3.84 \times {10^6}\]
(D) \[3840 \times {10^2}\]

Answer 1

Hint:Scientific notation is a way of writing down very large or very small numbers easily.
\[{10^3} = 1000\], 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, \[1 \leqslant m < 10\].

Complete step-by-step answer:
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 \[3.84 \times {10^6}\].

So, the correct answer is “Option C”.


Note:Scientific notation is a way of expressing real numbers that are too large or too small to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form in the UK.
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.