Math-Science Module: Scientific Notation
Name___________________________ Class__________ Date_________ Row_____
Very large or small numbers can be difficult to read and understand. They are easier to
understand and manipulate in exponential or scientific notation, that is in the form
c x 10b
for example 3.0 x 108 m/s is the speed of light, and 1.67 x 10-27 kg is the
proton mass
The number c is called either the coefficient, the mantissa, or the simple number, while b
is the exponent. In conventional, or normalized, scientific notation the number c must be
between 1 and 10. However, when adding or subtracting numbers in scientific notation it
is often convenient to change the exponent and mantissa so that the exponents in the
numbers being combined are the same; then the mantissa of one of them would not be
between 1 and 10.
A number in scientific notation can easily be converted to another exponent, for example
by moving the decimal in the mantissa one place to the right and subtracting one from
the exponent (or moving the decimal to the left and adding one to the exponent):
3.5 x 10-5 is the same as 35 x 10-6 or 0.35 x 10-4
Numbers in scientific notation are multiplied by multiplying the mantissas and adding the
exponents:
(3.5 x 10-5)(2.7 x 108) = (3.5)(2.7) x 10(-5+8) = 9.45 x 103
Scientific notation numbers are divided by dividing the mantissas and subtracting
exponents:
(2.4 x 109) ÷ (3.0 x 10-5) = (2.4/3.0) x 10(9-(-5)) = 0.8 x 1014 = 8.0 x 1013
Practice with Scientific Notation
1. Convert to conventional scientific notation
(a) 567,000 _________________
(b) 0.00043 __________________
(c) 4,877,000 _________________
(d) 0.00000839 ________________
(e) 49.4 x 10-2
________________
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(f) 0.67 x 10 _________________
(g) 0.0023 x 10-5 ________________
2. Multiply and convert answer to conventional form
(a) (3.87 x 10-3 )x(7.2 x 10-8) = ___________________
(b) (1.45 x 1010 )x(6.93 x 10-4 )= ______________________
(c) (7.2 x 1018 )x(2.5 x 10-21 ) =_______________________
(d) (3.455 x 1012)x(5.66 x 1017)= _______________________
(e) 479.8 x (3.8 x 107) _________________________________
3. Divide and convert to conventional form
(a) (6.98 x 109 ) ÷ (3.2 x 105 ) =______________________________________
(b) (5.76 x 105 ) ÷ (3.99 x 10-3) =_____________________________________
(c) (1.2 x 10-7 ) ÷ (6.78 x 108) =________________________________________
(d) (3.8 x 10-6) ÷ (8.66 x 10-4 )= _______________________________________
4. Combination calculations. Calculate
(a) (5.8 x 10-7) x (8.6 x 104 ) ÷ (3.22 x 10-9) =______________________________
(b) (2.1 x 1011) x (2.33 x 10-17) ÷ [(1.49 x 10-5) x ( 7.5 x 106 )] =
5. Addition and subtraction. Calculate
(a) (6.7 x 10-5) + (2.1 x 10-4) =
(b) (5.66 x 108) – (9.81 x 107)=
6. Calculations involving exponentiation [ remember that
(a) (3.2 x 1024 ) x (4.5 x 1022) ÷ (6.7 x 109)2 =
(c) (9 x 109) x (2.1 x 10-6) (4.5 x 10-5 ) ÷ 4(1.8 x 10-2)2 =
( cxa )b = cbxab ]