Prealgebra, Chapter 6 Decimals: 6.3 Multiplying Decimal Numbers; Exponents with Decimal Bases Objective 1: Multiply decimal numbers
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To multiply decimal numbers
o Stack the numbers, but it is not necessary to align the place values
o Multiply just like you would whole numbers
o Place the decimal point in the product so that it has the same
number of decimal places as the total number of decimal places in
the problem
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(2.31)(1.7)
Objective 2: Multiply signed decimal numbers
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Multiply in the same way as above, but remember that if you have an even
number of negative numbers in the problem your answer is positive, but if
you have an odd number of negative signs in the problem your answer is
negative
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(0.09)(-0.051)
Objective 3: Evaluate exponential forms with decimal bases
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Because an exponent tells us to repeatedly multiply the base, we must be
careful about the placement of the decimal point]
The easiest way to determine how many times to move the decimal point
is to count out the number of places in the base number and then multiply
that number by the exponent
•
Resource: Carson, T. (2009 ). Prealgebra – 3rd ed..
Prealgebra, Chapter 6 Decimals: 6.3 Multiplying Decimal Numbers; Exponents with Decimal Bases Objective 4: Write a number in scientific notation in standard form
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Scientific notation – A notation composed of a decimal number whose
absolute value is greater than or equal to “1” but less than “10”, multiplied
by 10 raised to an integer exponent
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To change from scientific notation to standard notation, move the decimal
point to the right the number of places indicated by the exponent
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8.23 ×
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-5.1782 ×
Objective 5: Write standard form numbers in scientific notation
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To write standard form numbers in scientific notation
o Move the decimal point so that the number’s value is grater than 1
but less than 10 (Put the decimal point to the right of the first
nonzero digit)
where n is the
o Write the decimal number multiplied by
number of places that you moved the decimal point
o Delete any zero’s to the right of the last nonzero digit
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417,000,000,000
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-2,917,300,000
Resource: Carson, T. (2009 ). Prealgebra – 3rd ed..
Prealgebra, Chapter 6 Decimals: 6.3 Multiplying Decimal Numbers; Exponents with Decimal Bases Objective 6: Multiply monomials
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We multiply decimal monomials the same way we multiply regular
monomials
Recall section 3.4; Multiply the coefficients and add the exponents of like
variables
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Objective 7: Multiply polynomials
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We multiply decimal polynomials the same way we multiply regular
polynomials
Recall section 3.4; Multiply polynomials using the distributive property
•
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(3.1n – 2)(1.7n + 6.5)
Resource: Carson, T. (2009 ). Prealgebra – 3rd ed..
Prealgebra, Chapter 6 Decimals: 6.3 Multiplying Decimal Numbers; Exponents with Decimal Bases Objective 8: Solve applications
• Remember to look for key words that signal multiplication and/or division
o Multiplication – Multiple, times, product, each, of, by
o Division – Divide, distribute, each, split, quotient, into, per, over
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Unit Price – The price of each unit
Resource: Carson, T. (2009 ). Prealgebra – 3rd ed..