Express the number in standard notation.
$6.83 \times 10^6$
Answer (2)
The number 6.83 × 1 0 6 in standard notation is 6 , 830 , 000 , obtained by multiplying 6.83 by 1,000,000 and moving the decimal point six places to the right. This conversion makes it easier to read large numbers. Standard notation is useful for expressing very large values clearly.
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We have a number in scientific notation: 6.83 × 1 0 6 .
To convert it to standard notation, we multiply 6.83 by 1 0 6 which equals 1,000,000.
Multiplying by 1 0 6 is the same as moving the decimal point 6 places to the right.
Therefore, 6.83 × 1 0 6 in standard notation is 6 , 830 , 000 .
Explanation
Understanding Scientific Notation We are given a number in scientific notation, which is a way of expressing numbers that are too big or too small to be conveniently written in standard notation. The number we have is $6.83
\times 10^6$. Our goal is to convert this into standard notation.
Converting to Standard Notation To convert from scientific notation to standard notation, we need to multiply the decimal number (6.83 in this case) by the power of 10 ( 1 0 6 in this case). Since 1 0 6 equals 1,000,000, we are essentially multiplying 6.83 by 1,000,000. This is equivalent to moving the decimal point 6 places to the right.
The Result So, we start with 6.83 and move the decimal point six places to the right. This gives us 6,830,000.
Final Answer Therefore, the number 6.83 × 1 0 6 in standard notation is 6,830,000.
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 × 1 0 13 kilometers. Writing this in standard notation as 40,170,000,000,000 kilometers is not only cumbersome but also makes it harder to quickly grasp the scale. Similarly, in chemistry, the Avogadro's number is approximately 6.022 × 1 0 23 , representing the number of atoms or molecules in a mole of a substance. Using scientific notation simplifies these representations and calculations.
