Question

How do you write \[3.77\times {{10}^{4}}\] in standard notation?

Answer 1

Hint: In this problem, we have to convert the scientific notation to the normal or standard notation. We should know that in scientific notation, a number is written as \[a\times {{10}^{n}}\], where n is an integer. To convert the scientific notation to its standard form, we just need to multiply the power \[{{10}^{n}}\], this means moving the decimal point n digits to the right if multiplying or to the left if dividing. In this problem, we can multiply 4 times 10 to the number 3.77 by moving the decimal point right side, to get the standard form.

Complete step by step answer:
We know that, the given scientific notation to be converted into a standard notation is,
\[3.77\times {{10}^{4}}\]
We know that, \[{{10}^{4}}\] can be written as 10000.
We can write 1000 instead of \[{{10}^{4}}\] in the given scientific notation, we get
\[\Rightarrow 3.77\times 10000\]
Now we can multiply both the numbers, we get
\[\Rightarrow 3.770000\]
We can now move the decimal, 4 points to the right, we get
\[\Rightarrow 37700.00\]
Therefore, the standard notation of \[3.77\times {{10}^{4}}\] is \[37700\].

Note:
Students make mistakes moving the decimal point, which should be concentrated. We should also know that, while converting the scientific notation to standard notation, if we multiply the decimal number with \[{{10}^{n}}\], we have to move the decimal point n digits to the right side, if we divide the decimal number with \[{{10}^{n}}\], we have to move the decimal point n digits to the left side.