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How do you convert \[3.14 \times {10^{ - 7}}\] to standard form?

Last updated date: 28th Feb 2024
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IVSAT 2024
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Hint: We are given a number that is written in scientific notation, it is a method used for convenient expression of too large or too small numbers in the decimal form. The scientific notation of a number is of the form $N \times {10^m}$ where N lies between 1 and 10 and involves only significant figures. In the given question, we have to convert the number written in scientific notation into standard form, so to do that we simply multiply the decimal number with the power of 10, in this question, there is no decimal involved so the calculation is easy and we have to write ${10^{ - 7}}$ in simplified form and then multiply it with the number 3. We can find the correct answer using this information.

Complete step-by-step solution:
We know that ${10^{ - 7}} = \dfrac{1}{{{{10}^7}}}$
\[{10^7}\] means 10 multiplied with itself 7 times, so –
  {10^7} = 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \\
   \Rightarrow {10^7} = 10000000 \\
  3 \times {10^{ - 7}} = 3 \times \dfrac{1}{{{{10}^7}}} \\
   \Rightarrow 3 \times {10^{ - 7}} = \dfrac{3}{{10000000}} \\
   \Rightarrow 3 \times {10^{ - 7}} = 0.0000003 \\

Hence, we can write $3 \times {10^{ - 7}}$ in standard notation as $0.0000003$.

Note: The number given in the question has a negative exponent; the negative exponent can be converted into a positive exponent by writing it as its own reciprocal. We first write the digits in decimal form, and the decimal point is placed after the first digit, and the digits after the decimal point are rounded off followed by the multiplication with 10 raised to the power number of digits that decimal places is moved to. The given number is written in scientific notation and we have to convert it into the standard notation so we follow the inverse process. This way we can solve all the questions similar to this one.