Operations in Scientific Notation

Operations in Scientific Notation

 $\left(a\times10^x\right)\times\left(b\times10^y\right)$  
 $=\left(a\times b\right)\times\left(10^x\times10^y\right)$  
 $=\left(a\times b\right)\times10^{\left(x+y\right)}$  

Multiplying in scientific notation:
-multiply the leading numbers
-add the exponents

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Multiplying in scientific notation

• Multiply the leading number

• Add the exponents

 $\left(a\times10^x\right)\div\left(b\times10^y\right)$  
 $=\left(a\div b\right)\times\left(10^x\div10^y\right)$  
 $=\left(a\div b\right)\times10^{\left(x-y\right)}$  

Dividing in scientific notation:
-divide the leading numbers
-subtract the exponents

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Dividing in scientific notation

• Divide the leading number

• Subtract the exponents

Practice!

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Multiple Choice

Multiply:

 $\left(6\times10^3\right)\times\left(2\times10^{10}\right)$  

•  $\left(6\times2\right)\times10^{\left(3+10\right)}$  

•  $\left(6+2\right)\times10^{\left(3+10\right)}$  

•  $\left(6\times2\right)\times10^{\left(3\times10\right)}$  

•  $\left(6+2\right)\times10^{\left(3\times10\right)}$  

Multiple Choice

Multiply:

 $\left(4\times10^5\right)\times\left(6\times10^1\right)$  

•  $\left(4\times6\right)\times10^{\left(5\times1\right)}$  

•  $\left(4\times6\right)\times10^{\left(5+1\right)}$  

Multiple Choice

Multiply:

 $\left(5\times10^4\right)\times\left(3\times10^2\right)$  

•  $\left(5+3\right)\times10^{\left(4+2\right)}$  

•  $\left(5\times3\right)\times10^{\left(4+2\right)}$  

Multiple Choice

Divide:
 $\left(6\times10^{10}\right)\div\left(2\times10^3\right)$  

•  $\left(6\div2\right)\times10^{\left(10-3\right)}$  

•  $\left(6\div2\right)\times10^{\left(10\div3\right)}$  

Multiple Choice

Divide:
 $\left(12\times10^6\right)\div\left(4\times10^2\right)$  

•  $\left(12-4\right)\times10^{\left(6-2\right)}$  

•  $\left(12\div4\right)\times10^{\left(6-2\right)}$  

Multiple Choice

Divide:
 $\left(9\times10^5\right)\div\left(3\times10^4\right)$  

•  $\left(9\div3\right)\times10^{\left(5\div4\right)}$  

•  $\left(9\div3\right)\times10^{\left(5-4\right)}$