Write the number -0.0000000463 in scientific notation.

Step-by-step solution

1. 1

   Separate the sign from the magnitude. Scientific notation is $a\times 10^{n}$ with $1\le |a|<10$. The minus sign is a property of the number, not of the exponent, so set it aside and convert $0.0000000463$ first, then restore the sign at the end.

2. 2

   Move the decimal point until the coefficient is between 1 and 10. Starting from $0.0000000463$, shift right past the zeros:

   $0.0000000463\to 4.63$

   Count the shifts: $0.0\underline{0000004}63$ — the point passes $8$ digit positions.

3. 3

   Choose the sign of the exponent from the direction of the shift. Moving the point to the right makes the coefficient larger, so the power of ten must make it smaller again: the exponent is $-8$, giving $4.63\times 10^{-8}$. Writing $10^{+8}$ here is the classic sign slip.

4. 4

   Restore the leading minus sign.

   $-0.0000000463=-4.63\times 10^{-8}$

   The coefficient $-4.63$ still satisfies $1\le|-4.63|<10$, so the form is valid.

5. 5

   Check by expanding back. $4.63\times 10^{-8}=4.63/100{,}000{,}000=0.0000000463$, and with the sign, $-4.63\times10^{-8}=-0.0000000463$ ✓. Counting zeros between the decimal point and the $4$ gives $7$, one fewer than the exponent's magnitude — a fast sanity check for any number written as $a\times10^{-n}$.