Question

answer the following. (A) an astronomers infrared telescope is able to detect radiation with a wavelength of 9.57 x 10^4 meters. Write this number in standard notation. (B) the diameter of mercury at its equator is approximately 4880 kilometers. Write this number in scientific notation.

Answer 1

A)

The number given,

`9.57*10^(-4)`

We need to write it in standard form.

Since the power of 10 is -4, we need to take the decimal point (from 9.57) four places to the left . So,

`\begin{gathered} 9.57*10^(-4) \\ =0.000957 \end{gathered}`B)

We need to write 4880 in scientific notation.

There is an invisible decimal point after the number, always.

We take that decimal point left until we have 1 digit before the decimal.

A little rough diagram might help:

Thus, the number in scientific notation will be 4.88.

The power of 10 will be 3, since we have to move three units right to arrive at our number.

So,

`\begin{gathered} 4880 \\ =4.88*10^3 \end{gathered}`