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Multiply numbers written in scientific notation

To multiply numbers in scientific notation, regroup to multiply the factors and multiply the powers of ten. Then simplify. To multiply the powers of ten, use the Product of Powers .

Evaluate the expression (1.3 x 102)(2.5 x 101).

 (1.3 x 102)(2.5 x 101) = (1.3 x 2.5)(102x101) Commutative and Associative Properties = (3.25)(102x101) Multiply 1.3 by 2.5. = 3.25x102+1 Product of Powers = 3.25x103 Add the exponents. = 3.25x1,000 103=1,000 = 3,250 Move the decimal point 3 places.

Evaluate the expression (4.2x103)(1.6x104).

 (4.2x103)(1.6x104) = (4.2x1.6)(103x104) Commutative and Associative Properties = (6.72)(103x104) Multiply 1.3 by 2.5. = 6.72x103+4 Product of Powers = 6.72x107 Add the exponents. = 6.72x10,000,000 107=10,000,000 = 67,200,000 Move the decimal point 7 places.

Evaluate the expression 3(2.5x104).

Multiply the coefficient 2.5 by 3, and adjust the exponent of 10 if needed. Note that we do not multiply both factors by 3, since no addition or subtraction is involved.

 3(2.5x104) = 3(2.5)x104 Multiply the coefficient by 10 = 7.5x104 The coefficient is still between 1 and 10, so no adjustment is needed.