What is $4.05 \times 10^6$ written in standard form?
Answer (1)
We are given the number 4.05 × 1 0 6 in scientific notation.
To convert it to standard form, we multiply 4.05 by 1 0 6 which equals 1,000,000.
Multiplying 4.05 × 1 , 000 , 000 results in 4,050,000.
Therefore, the standard form of 4.05 × 1 0 6 is 4 , 050 , 000 .
Explanation
Understanding Scientific Notation We are asked to convert the number $4.05
\times 10^6 f ro m sc i e n t i f i c n o t a t i o n t os t an d a r df or m . S c i e n t i f i c n o t a t i o ni s a w a yo f w r i t in gv ery l a r g eor v erys ma ll n u mb ers ina co m p a c t f or m . A n u mb er in sc i e n t i f i c n o t a t i o ni s w r i tt e na s a \times 10^b$, where $1
\leq |a| < 10 an d b i s anin t e g er . T oco n v er t an u mb er f ro m sc i e n t i f i c n o t a t i o n t os t an d a r df or m , w es im pl y m u lt i pl y a$ by 1 0 b .
Converting to Standard Form In this case, we have $4.05
\times 10^6$. This means we need to multiply 4.05 by 1 0 6 , which is 1,000,000. Multiplying by 1 0 6 is the same as moving the decimal point 6 places to the right.
Final Answer So, we have $4.05
\times 10^6 = 4.05
\times 1,000,000 = 4,050,000$. Therefore, $4.05
\times 10^6$ written in standard form is 4,050,000.
Examples
Scientific notation is extremely useful in fields like astronomy and physics, where you often deal with very large or very small numbers. For example, the distance to the nearest star, Proxima Centauri, is about $4.017
\times 10^{13}$ kilometers. Writing this number in standard form (40,170,000,000,000 km) is not only cumbersome but also makes it harder to grasp the scale. Similarly, the mass of an electron is about $9.109
\times 10^{-31}$ kilograms. Using scientific notation simplifies these numbers and makes calculations easier.
