Aim: To convert from ordinary notation to scientific notation & vice versa
Standard(s): 7.N.5, 7.N.6, 7.N.7
Pg 97 – 99 in workbook
Scientific Notation
... is a way to express very small or very large numbers.
... is most often used in "scientific" calculations where the analysis must be very precise.
... consists of two parts*:
1) a number between 1 and 10
2) a power of 10
To Change from Standard Form to Scientific Notation
1) Place decimal point such that there is one non-zero digit to the left of the decimal point.
2) Count number of decimal places the decimal has "moved" from the original number.
{This will be the exponent of the 10}
***If the original number was less than 1, the exponent is negative; if the original number was greater than 1, the exponent is positive.
Example(s):
Express in scientific notation:
1) 4,750,000
4.75 (moved 6 decimal places)
4.75 x 10
6
** The original number was greater than 1 so the exponent is positive.
2) 0.000789
7.89 (moved 4 decimal places)
7.89 x 10
–4
** The original number was less than 1 so the exponent is negative.
3) 23,600
2.36 x 10
4
is correct scientific notation
23.6 x 10
3
is not correct scientific notation

To Change from Scientific Notation to Standard Form:
1) Move decimal point to right for positive exponent of 10.
2) Move decimal point to left for negative exponent of 10.
Example(s):
Change the following to standard form:
1) 1.015 x 10
–8
** Negative exponent move decimal to the left.
0.00000001015
(8 places to left)
2) 5.024 x 10
3
**Positive exponent move decimal to the right.
5,024 (3 places to right)
Express in correct scientific notation:
1) 61, 500 = 6.15 x 10
4
2) 0.0000568 = 5.68 x 10
-5
3) 321 = 3.21 x 10
2
4) 64,960,000 = 6.496 x 10
7
5) 0.07085 = 7.085 x 10
2
Express in standard form:
1) 1.09 x 10
3
= 1090
2) 4.22715 x 10
8
= 422,715,000
3) 3.078 x 10
– 4
4) 9.004 x 10
–2
5) .1874 x 10
2
=
= .09004
=
.0003078
18.74
Put the following in order from least to greatest:
6.13 x 10
2
5.68 x 10
-4
3.11 x 10
1
6.46 x 10
4
3.85 x 10
-5
(4) (2) (3) (5) (1)
Scientific Cards Line up
An index card with a variety of numbers written in scientific notation will be given to each student. The class will then be asked to arrange themselves around the room in numerical order.
Additional activities:
• Ask all of the students holding numbers greater than one to move to one side of the room, and all students holding numbers less than one to move to the opposite side of the room.
• Ask 5 students to stand in the front of the room in numerical order. You, the teacher, holding a card, position yourself in the number line. Ask the class if you are standing in the correct numerical location.
**Thanks to regentsprep.org