Write the number -4.34 x 10^-2 in decimal notation without the use of exponents.

Step-by-step solution

1. 1

   Separate the sign from the magnitude. The leading minus belongs to the number itself, not to the power of ten. Convert $4.34\times 10^{-2}$ and reattach the sign at the end — this prevents the common error of treating the two minus signs as cancelling.

2. 2

   Read the direction from the sign of the exponent. A negative exponent makes the number smaller, so the decimal point moves left; a positive exponent moves it right. The exponent is $-2$, so the point moves $2$ places left.

3. 3

   Move the point, padding with zeros. Starting from $4.34$:

   $4.34\ \to\ 0.434\ \to\ 0.0434.$

   Two moves are needed and only one digit sits to the left of the point at the start, so one zero has to be inserted as a placeholder.

4. 4

   Reattach the sign.

   $-4.34\times 10^{-2}=-0.0434.$

5. 5

   Verify by reversing the conversion. $-0.0434$ has its first significant digit in the hundredths place, so writing it back in scientific notation gives $-4.34\times 10^{-2}$. Equivalently, $-4.34\div 100=-0.0434$.