Express the number in standard notation.
$8.127 \times 10^{-4}$
Answer (1)
The number is given in scientific notation as 8.127 × 1 0 − 4 .
To convert from scientific notation to standard notation, move the decimal point in 8.127 four places to the left since the exponent of 10 is -4.
This gives 0.0008127.
Therefore, the number in standard notation is 0.0008127 .
Explanation
Understanding Scientific Notation We are given the number $8.127
\times 10^{-4} in sc i e n t i f i c n o t a t i o nan d w e w an tt oe x p ress i t in s t an d a r d n o t a t i o n . S c i e n t i f i c n o t a t i o ni s a w a yo f w r i t in gv ery l a r g eor v erys ma ll n u mb ers ina co m p a c t f or m . A n u mb er in sc i e n t i f i c n o t a t i o ni s w r i tt e na s a
\times 10^{b}$, where $1
\leq |a| < 10 an d b$ is an integer.
Converting to Standard Notation To convert from scientific notation to standard notation, we need to move the decimal point in 8.127 four places to the left because the exponent of 10 is − 4 . Moving the decimal point one place to the left gives 0.8127 . Moving it two places to the left gives 0.08127 . Moving it three places to the left gives 0.008127 . Moving it four places to the left gives 0.0008127 .
Final Answer Therefore, $8.127
\times 10^{-4} = 0.0008127$.
Examples
Scientific notation and standard notation are useful in many real-world applications, especially in science and engineering. For example, the size of a bacteria might be 2 × 1 0 − 6 meters, which is 0.000002 meters in standard notation. Similarly, the distance to a star might be 4.3 × 1 0 16 meters, which is a very large number in standard notation. Using scientific notation makes it easier to work with these very small or very large numbers.
