Name: ____________________________________________
Scientific Notation
Date: __________________
How to find scientific notation:
1. Find your first NON-ZERO number, reading from left to right. Ex: 0.00042 (4 is your first
non-zero number)
2. Move the decimal place so that it is right after the first non-zero number. Ex: 0.0004.2
3. Count how many places you moved the decimal point. Ex: if you had to move 4 places
0.0004.2
4. Determine if your exponent should be positive or negative. If you moved the decimal to
the right your exponent is negative, but if it moved to the left the exponent is positive.
5. Your answer should be written with your constant multiplied by ten to a positive or
negative power. Ex: 4.2 × 10−4
Write the following numbers in scientific notation:
1) 0.00052 5.2 x 10-4
7) 6,077,900 6.0779 x 106
2) 2,897,000 2.897 x 106
8) 0.0012890 1.2890 x 10-3
3) 0.1234000 1.234 x 10-1
9) 5,000,000 5 x 106
4) 8,000,000,000 8 x 109
10) 0.0045098 4.5098 x 10-3
5) 4,876,000 4.876 x 106
11) 4,235,000,000 4.235 x 109
6) 0.00000678 6.78 x 10-6
12) 1,879,300,000,000 1.8793 x 1012
Doing the Math with Scientific Notation:
1. If you are multiplying you must multiply your factors and add your exponents.
2. If you are dividing you must divide your factors and subtract your exponents.
Complete the problems using the rules of scientific notation:
1) (10×105) × (2×103) 2.0 x 1014
4) (3×104) × (4×105) 1.2 x 1010
2) (6×103) ÷ (3×102) 2 x 101 (2)
5) (5×108) ÷ (2×103) 2.5 x 105
3)
(16×10-2)
÷
(4×103)
4x
10-5
Name: ____________________________________________
Scientific Notation
Date: __________________
Section A: Convert to scientific notation.
1. 1001 1.001 x 103
6. 0.13592 1.3592 x 10-1
7. -0.0038 -3.8 x 10-3
2. 53 5.3 x 101
3. 6,926,300,000 6.9263 x 109
4. -392 -3.92 x 102
5. 0.00361 3.61 x 10-3
8. 0.00000013 1.3 x 10-7
9. -0.567 -5.67 x 10-1
10. 93,000,000 9.3 x 107
Section B: Convert from scientific notation.
1. 1.92 x 103 1920
2. 3.00 x 108 300,000,000
3. -4.29 x 102 -429
4. 6.251 x 109 6,251,000,000
5. 8.317 x 106 8,317,000
6. 1.03 x 10-2 0.0103
7. 8.862 x 10-1 0.8862
8. 9.512 x 10-8 0.00000009512
9. -6.5 x 10-3 0.0065
10. 3.159 x 102 315.9
Section C: Arithmetic with scientific notation.
1. (4.1357 x 10-15) * (5.4 x 102) = 2.2332 x 10-12
2. (1.695 x 104) ÷ (1.395 x 1015) = 1.215 x 10-11
3. (4.367 x 105) * (1.96 x 1011) = 8.559 x 1016
4. (6.97 x 103) * (2.34 x 10-6) = 1.631 x 10-2
5. (8.0 x 10-3) + (3.2 x 10-2) = 4.0 x 10-2
6. (5.16 x 10-4) ÷ (8.65 x 10-8) = 0.597 x 104
7. (9.0 x 1023) + (9.0 x 1024) = 9.9 x 1024
Section D: Comparing powers. How many times bigger or smaller is the 1st than the 2nd?
1. 102 to 103
10 (101)x bigger/smaller
2. 1020 to 1023 1000 (103)x bigger/smaller
3. 10-2 to 10-1 10 (101)x bigger/smaller
4. 10-31 to 10-29 100 (102)x bigger/smaller
5. 1024 to 1030 1,000,000 (106)x bigger/smaller