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Multiply & Divide in Scientific NotationMultiply & Divide in Scientific Notation
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Question 1 of 5
1. Question
Multiply`(4.0xx 10^5)(3.2xx10^(3))`Provide your answer in numerical notation (1280)
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Scientific notation is a way to represent very large or very small numbers in a compact form. It is in the format: `a xx 10^n`.Multiply the numbers first and then the exponents of `10` separately.`(``4.0``xx`` 10^5``)(``3.2``xx``10^(3)``)``4.0``xx` `3.2``=``12.8` `(10^5)``xx` `(10^(3))``=``10^2` Multiplication property of exponents Combine the obtained values and simplify.`12.8`` xx`` 10^2` `=` `1.28xx 10^3` Move the decimal point one place to the left `=` `1280` Express in numerical notation `1280` 
Question 2 of 5
2. Question
Divide`(3.5xx 10^(7))/(7.0xx10^5)`Hint
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Scientific notation is a way to represent very large or very small numbers in a compact form. It is in the format: `a xx 10^n`.Divide the numbers first and then the exponents of `10` separately.$$\frac{\color\green{3.5} \times \color{#004ec4}{10^{7}}}{\color\green{7.0} \times \color{#004ec4}{10^5}}$$`3.5/7.0``=``0.5` `(10^(7))/(10^5)``=``10^(75)``=``10^(12)` Division property of exponents Combine the obtained values and simplify.`0.5`` xx`` 10^(12)` `=` `5xx 10^(13)` Move the decimal point one place to the right `5 xx 10^(13)` 
Question 3 of 5
3. Question
Divide`((7.5xx 10^(4))(3.2 xx 10^5))/(3.75xx10^9)`Provide your answer in numerical notation (0.000000064)
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Excellent!
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Scientific notation is a way to represent very large or very small numbers in a compact form. It is in the format: `a xx 10^n`.Multiply and divide the numbers first and then the exponents of `10` separately.$$\frac{(\color\green{7.5} \times \color{#004ec4}{10^{4}})(\color\green{3.2} \times \color{#004ec4}{10^5})}{\color\green{3.75} \times \color{#004ec4}{10^9}}$$`(7.5xx3.2)/3.75``=``6.4` `((10^(4))xx10^5)/(10^9)``=``(10^(4+5))/(10^9)``=``(10^1)/(10^9)``=``10^(8)` Multiplication and Division property of exponents Combine the obtained values and simplify.`6.4`` xx`` 10^(8)` `=` `0.000000064` Express in numerical notation `0.000000064` 
Question 4 of 5
4. Question
Multiply`0.0064 xx 0.0000071`Hint
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Fantastic!
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Scientific notation is a way to represent very large or very small numbers in a compact form. It is in the format: `a xx 10^n`.Convert the numbers into scientific notation.`0.0064` `=` `6.4 xx 10^(3)` Move the decimal point `3` places to the right `0.0000071` `=` `7.1 xx 10^(6)` Move the decimal point `6` places to the right Multiply the numbers first and then the exponents of `10` separately.`(``6.4``xx`` 10^(3)``)(``7.1``xx``10^(6)``)``6.4``xx` `7.1``=``45.44` `(10^(3))``xx` `(10^(6))``=``10^(9)` Multiplication property of exponents Combine the obtained values and simplify.`45.44`` xx`` 10^(9)` `=` `4.544 xx 10^(8)` Move the decimal point one place to the left `4.544 xx 10^(8)` 
Question 5 of 5
5. Question
Multiply`0.032 xx 580000`Hint
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Exceptional!
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Scientific notation is a way to represent very large or very small numbers in a compact form. It is in the format: `a xx 10^n`.Convert the numbers into scientific notation.`0.032` `=` `3.2 xx 10^(2)` Move the decimal point `2` places to the right `580000` `=` `5.8 xx 10^5` Move the decimal point `5` places to the left Multiply the numbers first and then the exponents of `10` separately.`(``3.2``xx`` 10^(2)``)(``5.8``xx``10^5``)``3.2``xx` `5.8``=``18.56` `(10^(2))``xx` `(10^5)``=``10^3` Multiplication property of exponents Combine the obtained values and simplify.`18.56`` xx`` 10^3` `=` `1.856 xx 10^4` Move the decimal point one place to the left `1.856 xx 10^4`