Question

Answer the following(a) The diameter of Saturn at its equator is approximately 1.21x10 ^5 kilometers. Write this number in standard notation(b) An astronomer's infrared telescope is able to detect radiation with a wavelength of 0.00000835 meters. Write this number in scientificnotation(A)kilometers(b) meters

Answer 1

a) The exponent value of the scientific notation indicates the number of zeros you have to add to the number to write it in standard form.

The sign of the exponent indicates if the zeros are above or below the decimal dot.

If the exponent is positive, then the number is very large, this means that you have to move the decimal for to the right, to fill in the places you have to add zeros, for example:

`1.0\cdot10^(10)=10000000000.`

The exponent "10" indicates that behind the number 1 there are ten zeros.

If the exponent is negative, then the number is very small, for example:

`1.0\cdot10^(-9)=0.000000001`

You have to move the decimal dot 9 places to the left.

• The diameter of Saturn is:

`1.21\cdot10^5`

Move the decimal dot 5 places to the right

The number expressed in standard notation is:

`1.21\cdot10^5=121000km`

b) Given the value: 0.00000835

To express this value in scientific form, you have to move the decimal dot to the right until after the first digit different to zero.

Count the number of places you moved the decimal dot, this value will represent the exponent of the scientific notation. The number is less than one, so the exponent will be negative:

You have to move the decimal dot 6 places to the right, the exponent of the scientific notation will be -6

`0.00000835=8.35\cdot10^(-6)m`