Download 1-Scientific notation worksheet

SCIENTIFIC NOTATION WORKSHEET
PART A: Convert the following full numbers into scientific notation. (ANSWERS IN BOLD)
1.
65.7
2.
0.00545
(6.57 X 101)
(5.45 X 10-3)
3.
1 100 000 000 km/h
(Speed of light)
4.
40 100 000 m
(Circumference of the earth)
(1.1 X 109 km/h)
5.
0.0001 m
(Width of an ant’s eye)
(4.01 X 107 m)
6.
0.000 000 000 2 m
(Width of a hydrogen atom)
(1 X 10-4 m)
7.
-22 450 000 m/s2
(2 X 10-10 m)
8.
- 0.000 000 000 000 775 290 12
(-2.245 X 107 m/s2)
(-7.7529012 X 10-13)
PART B: Convert the following from scientific notation to full numbers.
1.
1.7 X 101
2.
6.32 X 1023
(17)
3.
1 X 1012
(The number ‘a trillion’)
(632 000 000 000 000 000 000 000)
4.
9.47 X 108
(The number of seconds you’ve been
alive when you turn 30)
(947 000 000)
6.
5 X 10-8 m
(Width of an influenza virus)
(1 000 000 000 000)
5.
1 X 10-4 m
(Thickness of a piece of paper)
(0.000 1 m)
7.
-3.4 X 103
(0.000 000 05 m)
8.
(-3400)
9.
3.0 X 108 m/s2
(300 000 000 m/s)
-6.67 X 10-16
(-0.000 000 000 000 000 667)
10.
-1.99 X 100 h
(-1.99 h)
PART C: Perform the following calculations and express your final answer in scientific notation.
**
Rule for Multiplication - When you multiply numbers in scientific notation, multiply
the coefficients and add the exponents..
1.
Rule for Division - When dividing numbers in scientific notation, divide the coefficients
and subtract the exponents.
(6.8 X 103)(4.54 X 106)
2.
(2.0 X 10 -1)(8.5 X 105)
(3.08 X 1010)
3.
(4.42 x 10-3) x (-4 x 10-2)
(1.7 X 105)
4.
(-1.76 X 10-4)
5.
(-8.61 X 10-10) ÷ (-5.89 X 10-7)
(9.2 X 10-3) ÷ (6.3 X 106)
(1.46 X 10-9)
6.
(1.46 X 10-3)
(-6.11 X 1034) ÷ (7.48 X 10-11)
(-8.168 X 1044)
PART D: Perform the following calculations and express your final answer in scientific notation.
**
Rule for Addition and Subtraction - when adding or subtracting numbers in scientific
notation, you must express all of the numbers to the same power of 10. This will often
involve changing the decimal place of one or more coefficients. After doing this you add
the coefficients and leave the common exponent.
1.
(2.3 X 105) + (1.0 X 106)
2.
(5.66 X 10-4) + (7.2 X 10-6)
(1.23 X 106)
3.
(7.0 X 10-2) - (4.23 X 10-3)
(5.732 X 10-4)
4.
(6.577 X 10-2)
5.
(6.423 x 101) + (-5.001 x 10-1)
(1.95 X 1015)
6.
(6.373 X 101)
7.
(-8.23 x 104) - (-3.02 x 105)
(2.197 X 105)
(1.99 X 1015) - (3.99 X 1013)
(4.54 x 107) - (-1.01 x 108)
(1.464 X 108)
8.
(7.83 x 10-2) - (2.20 x 10-5)
(7.83 X 10-2)