Question

Answer the following.(a) An astronomer's infrared telescope is able to detect radiation with a wavelength of 1.96 x 10^-5 meters. Write this number in standardnotation(b) The diameter of Venus at its equator is approximately 12,100 kilometers. Write this number in scientific notation.(a) Imeters(b) kilometers

Answer 1

a)

We need to convert 1.96 x 10^-5 meters. into standard notation.

Now, on the scientific notation, the power of ten shows how many places the decimal point has been moved.

- If the exponent is positive then the decimal point has been moved to the left.

- If the exponent is negative, then the decimal point has been moved to the right.

In this case, the power is negative 5 . So, the decimal point has been moved 5 places to the right.

Hence:

1.96 x 10^-5 = 0.0000196

b)

a. Meters

First, we need to convert kilometers into meters using the rule of three:

If 1k = 1000 meters

Then 12,100k = x

Where x = (12,100k*1000m)/ 1k

x =12000000 meters

We need to convert from standard notation to scientific notation:

12000000.0 = 1.2x10^7 meters

The decimal point has been moved 7 places to the left, so the power of then is positive 7.

b) We need to convert 12,100 kilometers into scientific notation:

12,100 = 12,100.0

Converting into scientific notation

1.21x10^4 kilometers

The decimal point has been moved 4 places to the left. Hence, the power of the is positive 4.