8th Grade AR – Scientific Notation
7 Lesson Date ______
Warm Up (5 mins): Have students answer the following exponent problems:
1.) 72 = 49 2.) 104 = 10,000 3.) 107 = 10,000,000 4.) 53 = 125
Lesson (20 mins):
Scientific Notation is a special way of writing numbers. It is used in many different fields of Science to show both very large and very small numbers.
Here are 3 numbers and their equivalents in scientific notation:
230,000 = 2.3 x 105
0.00000105 = 1.05 x 10-6
4,761,000,000 = 4.761 x 109
A number in scientific notation has two factors: The first factor is a number greater than or equal to 1 and less than 10. The second factor is a power of 10 (10 with an exponent). The exponent can be either positive or negative. o A positive exponent indicates the number of times 10 is used as a factor. Very large numbers get positive exponents. o A negative exponent indicates the number of times 10 is used as a divisor. Very small numbers get negative exponents.
For example: 230,000 = 2.3 x 105
First Second Factor Factor
Revised October 2007 8th Grade AR – Scientific Notation
Show example #1:
Saturn is about 875,000,000 miles from the sun. How would this distance be represented in scientific notation?
1.) Write the first factor by using the 3 non – zero digits (875) of 875,000,000. Place the decimal point after the first digit: The first factor becomes 8.75 Remember, this factor is a number greater than 1 but less than 10.
2.) Write the second factor. What number times 8.75 equals 875,000,000? The number is 100,000,000 or 108, so 108 is the second factor. OR Quick way: Count the number of decimal places after the first digit in 875,000,000. There are 8 decimal places, so the exponent of 10 is 8: 108.
3.) Write the two factors together:
875,000,000 = 8.75 x 108 4.) Answer: The distance of Saturn from the sun is 8.75 x 108 miles.
****NOTE: The exponent 8 in the answer represents 8 places to the left from the original decimal point in 875,000,000.
8.75,000,000. Count 8 places to the left
Show example #2:
Write 0.00017 in scientific notation.
1.) Find the first factor. Use the two non-zero numbers 1 and 7. First factor: 1.7
2.) Count from the original decimal point to the new decimal point to find the exponent.
0.0001.7 = count 4 places…The exponent will be negative because you count to the right and the original number is a very small number.
3.) Write the factors together. Revised October 2007 1.7 x 10-4 8th Grade AR – Scientific Notation
Show Example #3:
The height of a building is about 5,300 feet. Express this height in Scientific notation.
1.) Write the first factor as a number between 1 and 10.
5.3
2.) Determine the factor of 10.
You count 3 places to the left from the original decimal point, so the exponent is positive 3.
3.) Solution:
5.3 x 103 Show Example #4:
Express 0.0345 in scientific notation
1.) Write the first factor as a number between 1 and 10.
3.45
2.) Determine the factor of 10.
You count 2 places to the right from the original decimal point, so the exponent is negative 2.
3.) Solution:
3.45 x 10-2
Practice (15 minutes): Have students complete the Sample questions – Go over all answers. Remind students to show all work!!!
Closure (3 minutes): Have students put all work in their folders, and fill out reflection box on Agenda sheet. Have students return all folders to you until next week.
Revised October 2007 8th Grade AR – Scientific Notation Sample Questions: WORK AREA 1.) How would 4,500,000 be expressed in scientific notation?
A) 4.5 x 106 B) 4.5 x 107 C) 4.5 x 105 D) 450 x 104
2.) How would 0.0000326 be expressed in scientific notation?
F) 3.26 x 105 G) 3.26 x 10-5 H) 3.26 x 10-4 J) 3.26 x 104
3.) 5.624 x 10-4
A) 0.005624 B) 0.0005624 C) 5624 D) 56,240
4.) 500,000 x 6,000 =
F) 3 x 106 G) 3 x 107 H) 3 x 108 J) 3 x 109
5.) 3.28 x 10-2
A) 328 B) 0.328 C) 0.0328 D) 0.00328
6.) A microsecond is equal to 10-6 seconds. How many seconds (in decimal form) is 7 microseconds?
F) 7,000,000 G) 0.7000006 H) 0.000007 J) 0.0000007
7.) What is the value of 26?
A) 26 B) 32 C) 64 D) 128
Revised October 2007 8th Grade AR – Scientific Notation
8.) The planet Mars is 710,000,000 miles from the sun. What is this distance expressed in scientific notation?
F) 7.1 x 108 miles G) 7.1 x 107 miles H) 7.1 x 106 miles J) 7.1 x 10-7 miles
9.) A micron is a unit of measurement equivalent to 0.000039 inch. What is this distance expressed in scientific notation?
A) 0.39 x 10-4 inches B) 3.9 x 10-4 inches C) 3.9 x 10-5 inches D) 3.9 x 10-6 inches
10.) Which is 7,312 written in scientific notation?
F) 73.12 x 102 G) 7.312 x 102 H) 7.312 x 103 J) 73.12 x 10-2
11.) Which number represents 5.391 x 107 in standard form?
A) 5,391,000 B) 53,910,000 C) 539,100,000 D) 5,391,000,000
12.) What is 54 expressed in standard notation?
F) 20 G) 25 H) 125 J) 625
13.) A red blood cell is about 0.000273 inch wide. Which expresses this number in scientific notation?
A) 2.73 x 10-2 B) 2.73 x 10-4 C) 2.73 x 102 D) 27.3 x 10-4
Revised October 2007 8th Grade AR – Scientific Notation
14.) This number is written in scientific notation. What is the standard notation for this number?
3.21 x 10-1
15.) Choose the greater in each pair:
5.01 x 102 OR 5.02 x 10-1
16.) Choose the greater in each pair:
1.9 x 10-2 OR 0.02
17.) Choose the greater in each pair:
8.4 x 102 OR 839
18.) Choose the greater in each pair:
8.8 x 103 OR 9.1 x 10-4
19.) Choose the greater in each pair:
6.4 x 103 OR 900
20.) Choose the greater in each pair:
2.2 x 10-3 OR 2.1 x 102
Revised October 2007