What is $9.309 \times 10^{-3}$ written in standard form?
Answer (2)
We are given the number 9.309 × 1 0 − 3 in scientific notation.
To convert to standard form, multiply 9.309 by 1 0 − 3 , which is equivalent to dividing by 1000.
Moving the decimal point three places to the left gives 0.009309 .
Therefore, the standard form is 0.009309 .
Explanation
Understanding Scientific Notation We are given the number $9.309
\times 10^{-3} in sc i e n t i f i c n o t a t i o nan d w e w an tt oco n v er t i tt os t an d a r df or m . S c i e n t i f i c n o t a t i o ni s a w a yo f w r i t in gv ery l a r g eor v erys ma ll n u mb ers ina co m p a c t f or m . A n u mb er in sc i e n t i f i c n o t a t i o ni s w r i tt e na s a
\times 10^{b}$, where $1
\leq |a| < 10 an d b i s anin t e g er . T oco n v er t an u mb er f ro m sc i e n t i f i c n o t a t i o n t os t an d a r df or m , w e n ee d t o m u lt i pl y a$ by 1 0 b .
Multiplying by the Power of 10 In our case, we have $9.309
\times 10^{-3}$. This means we need to multiply 9.309 by 1 0 − 3 . Since 1 0 − 3 = 1 0 3 1 = 1000 1 = 0.001 , we are multiplying 9.309 by 0.001 .
Moving the Decimal Point Multiplying 9.309 by 0.001 is the same as moving the decimal point three places to the left. So, we have:
$9.309
\times 0.001 = 0.009309$
Final Answer Therefore, $9.309
\times 10^{-3}$ in standard form is 0.009309 .
Examples
Scientific notation is used in many fields, such as physics, astronomy, and chemistry, to represent very large or very small numbers. For example, the speed of light is approximately 3 × 1 0 8 meters per second, and the mass of an electron is approximately 9.11 × 1 0 − 31 kilograms. Converting between scientific notation and standard form helps us to better understand and compare these values. Imagine you're working with microscopic organisms, where sizes are often measured in micrometers ( 1 0 − 6 meters). Converting these measurements to standard form helps in visualizing and comparing the actual sizes of these organisms.
The number 9.309 × 1 0 − 3 in standard form is 0.009309 . This is achieved by moving the decimal point three places to the left due to the negative exponent. Thus, the final answer is 0.009309 .
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