Write the number -7.71 x 10^4 in decimal notation without the use of exponents.

Step-by-step solution

1. 1

   Set the sign aside. The minus belongs to the coefficient, not to the power of ten. Convert $7.71\times 10^{4}$ and put the sign back at the end.

2. 2

   Read the direction and the count from the exponent. The exponent $+4$ is positive, so the number is large and the decimal point moves 4 places right.

3. 3

   Move the point, appending zeros as placeholders. Starting from $7.71$, only two digits sit after the point, so after using them up you must supply zeros for the remaining moves:

   $7.71\to 77.1\to 771.\to 7710.\to 77100.$

4. 4

   Reattach the sign and add place separators.

   $-7.71\times 10^{4}=-77100=-77{,}100.$

5. 5

   Verify by reversing. Moving the point in $-77100$ back to just after the first significant digit takes $4$ places to the left, giving $-7.71\times 10^{4}$. Equivalently $-7.71\times 10000=-77100$.