Scientific Notation and Models
Change the following numbers into scientific notation
0.00345
_____________________
456700000000 _____________________
123.4 x 10-1
_____________________
0.0023 x 106
_____________________
Change the following numbers into standard notation
3.568 x1012
_____________________
6.58 x 10-6
_____________________
123.4 x 10-1
_____________________
0.0023 x 106
_____________________
When a number is in standard notation, what is the assumed exponent on the number? __________
Why can you assume that?
Complete the following table of rules for doing math with scientific notation. The first column lists the various math
operations you may do with scientific notation, the second column is what you do with the coefficients of the scientific
notation numbers when conducting the stated math operation, and the third column is what you do with the exponents.
Math Operation
Coefficients
Exponents
Multiplication
Subtraction
Raising to a Power
Addition
Taking a Root
Division
Of the math operations listed above, addition and subtraction are the ones which give people the most difficulty. What
must be done with the scientific notation numbers before you can carry out these two math operations?
Solve the following problems and put into correct scientific notation:
(4.09x104)5
_____________________
(6.23x10-2)-2
_____________________
(2.6x10-3)5
_____________________
(1.08x10-2)-2
_____________________
√(3.4x106)
_____________________
3
√(4.78x109)
_____________________
The table below provides information that will be useful in solving the problems on this page.
MERCURY
VENUS
EARTH
MOON
MARS
JUPITER
SATURN
URANUS
NEPTUNE
Mass (kg)
3.30x1023
4.87x1024
5.97 x1024
7.3 x1022
6.42 x1023
1.898 x1027
5.68 x1026
8.68 x1025
1.02 x1026
Diameter (km)
4.879 x103
1.2104 x104
1.2756 x104
3.475 x103
6.792 x103
1.42984
x105
1.20536
x105
5.1118 x104
4.9528 x104
Distance from
Sun (km)
5.79x107
1.082 x108
1.496 x108
3.84 x105*
2.279 x108
7.786 x108
1.4335 x109
2.8725 x109
4.4951 x109
* For the Moon, the average distance from the Earth is given.
Sun’s Diameter: 1.391x106
Sun’s Mass: 1.989x1030
For each problem below, set up the problem and show your work. The only time you should use a calculator is to carry
out the needed math operations on the coefficients.
If Mercury and Venus collided and formed a single planet (highly improbable), what would be the total mass of the new
planet?
The Earth and Moon were once part of the same planetary body. The Moon broke off of the Earth after an impact from
a large asteroid or comet. What was the total mass of the Earth BEFORE the Moon broke away?
If a similar event happened to Jupiter and knocked a chunk off of Jupiter the size of Uranus, what would the new mass of
Jupiter be?
How many Moon’s would fit across the diameter of the Earth?
How many Moon’s would fit between the Sun and the Earth?
If instead of being a certain number of Moons away from the Sun, we were an equal number of Saturns away from the
Sun, How far would the Earth be from the Sun?
A Light Year is a measure of distance and is equal to 5.85x1012 km. The next closest star to our Sun is Proxima Centauri,
which is 4.243 light years away. How far is Proxima Centauri away from the Sun in km?
How many Sun’s would fit between the Sun and Proxima Centauri?