Write the number -3.00008 x 10^9 in decimal notation without the use of exponents.

Step-by-step solution

1. 1

   Read off direction and distance from the exponent. The exponent $+9$ is positive, so the point moves nine places right and the result is a large number, in the billions.

2. 2

   Split the nine moves into two stages. The coefficient $3.00008$ has five digits after the point, so five moves consume those digits and the other four must be padded with zeros:

   $9=5+4.$

3. 3

   Stage one: move five places using the existing digits.

   $3.00008\to 30.0008\to 300.008\to 3000.08\to 30000.8\to 300008.$

   Each interior zero must be carried across in position; they are what keeps the $8$ in its correct place value.

4. 4

   Stage two: append four zeros.

   $300008\to 3000080000.$

5. 5

   Reattach the sign and group the digits.

   $-3.00008\times 10^{9}=-3000080000=-3{,}000{,}080{,}000.$

6. 6

   Check by reversing. Moving the point back to just after the leading $3$ takes nine places, giving $3.00008\times 10^{9}$ ✓. Equivalently $3.00008\times 1{,}000{,}000{,}000=3{,}000{,}080{,}000$.