Express the number in standard notation.
$2.7 \times 10^4$
Answer (2)
The number 2.7 × 1 0 4 in standard notation is 27,000. This was obtained by multiplying 2.7 by 10,000, which is the equivalent of 1 0 4 .
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We are given the number 2.7 × 1 0 4 in scientific notation.
To convert to standard notation, we multiply 2.7 by 1 0 4 which is 10,000.
Performing the multiplication, 2.7 × 10 , 000 = 27 , 000 .
The number in standard notation is 27000 .
Explanation
Understanding Scientific Notation We are given a number in scientific notation, $2.7
\times 10^4$, and we want to express it in standard notation. Scientific notation is a way of writing very large or very small numbers in a compact form. The number 1 0 4 represents 10 raised to the power of 4, which is 10,000. To convert from scientific notation to standard notation, we need to multiply the decimal number (2.7 in this case) by the power of 10 (which is 1 0 4 or 10,000).
Converting to Standard Notation To convert $2.7
\times 10^4 t os t an d a r d n o t a t i o n , w e m u lt i pl y 2.7 b y 10 , 000 : 2.7 × 10 , 000 = 27 , 000 $
This is equivalent to moving the decimal point in 2.7 four places to the right. Since we only have one digit after the decimal point, we need to add three zeros to the right of 7 to move the decimal point four places.
Final Answer Therefore, the number $2.7
\times 10^4$ in standard notation is 27,000.
Examples
Scientific notation is used in many real-world applications, especially when dealing with very large or very small numbers. For example, astronomers use scientific notation to express the distances between stars and galaxies. A light-year, the distance light travels in one year, is approximately 9.46 × 1 0 15 meters. Similarly, biologists use scientific notation to describe the size of cells or the concentration of molecules. The size of a typical bacterium might be 2 × 1 0 − 6 meters. Using scientific notation makes these numbers easier to work with and understand.
