How would you represent 0.006453 in standard scientific notation?
a) 0.006453
b) [tex]$6453 \times 10^{-6}$[/tex]
c) [tex]$64.53 \times 10^{-4}$[/tex]
d) [tex]$6.453 \times 10^{-3}$[/tex]
e) [tex]$0.6453 \times 10^{-2}$[/tex]
Answer (2)
To convert 0.006453 to scientific notation, you move the decimal point three places to the right, giving you 6.453. This means you express the number as 6.453 multiplied by 10 raised to the power of -3. Thus, the correct answer is 6.453 × 1 0 − 3 .
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Move the decimal point in 0.006453 three places to the right to obtain a number between 1 and 10, which is 6.453.
Since the decimal point was moved three places to the right, multiply by 1 0 − 3 .
Express 0.006453 in standard scientific notation as 6.453 × 1 0 − 3 .
The final answer is 6.453 × 1 0 − 3 .
Explanation
Understanding Scientific Notation We need to express the number 0.006453 in standard scientific notation. Standard scientific notation is a way of writing numbers as a product of a number between 1 and 10 (including 1) and a power of 10.
Moving the Decimal Point To convert 0.006453 to scientific notation, we need to move the decimal point until we have a number between 1 and 10. Moving the decimal point three places to the right gives us 6.453.
Determining the Exponent Since we moved the decimal point three places to the right, we need to multiply by 1 0 − 3 to compensate for the shift. This gives us 6.453 × 1 0 − 3 .
Final Result Therefore, 0.006453 in standard scientific notation is 6.453 × 1 0 − 3 .
Examples
Scientific notation is extremely useful in fields like physics and astronomy, where you often deal with very large or very small numbers. For example, the speed of light is approximately 3.0 × 1 0 8 meters per second, and the mass of an electron is approximately 9.11 × 1 0 − 31 kilograms. Writing these numbers in scientific notation makes them easier to handle and compare.
