Scientific Notation Operations      GO BACK TO CHEMISTRY DRILLS PAGE         *

Below are several calculations you should be able to make using scientific notation math rules.  After you finish each problem, click to see answers and work.
Compare yours to the correct answers.  Always watch out for significant figures!

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Add#1

3.45 x 10²⁴  +  2.13 x 10²⁴   =  5.58 x 10²⁴

Rule for addition: Make sure exponents are the same, add coefficients.

Both are 10²⁴, so add coefficients, keep 10²⁴. 

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Add#2

4.87 x 10¹²  +  3.90 x 10¹⁴

Rule:  Fix exponents to the same (either both 12 or 14) by adjusting the coefficients. 
Then add, adjust significant figures. 

4.87 x 10¹²  +  3.90 x 10¹⁴           becomes:

4.87 x 10¹²  +  390. x 10¹²  = 394.7 x 10¹²    or   3.95 x 10¹⁴

or    4.87 x 10¹²  +  3.90 x 10¹⁴           becomes:

 0.0487 x 10¹⁴  +  3.90 x 10¹⁴  = 3.947 x 10¹⁴    or   3.95 x 10¹²

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Add#3

9.93 x 10³  +  2.28 x 10⁴

Rule:  Fix exponents to the same (either both 3 or 4) by adjusting the coefficients. 
Then add, adjust significant figures.  THEN adjust coefficients to 1.0 to 9.9 accordingly.

9.93 x 10³  +  2.28 x 10⁴     becomes:

9.93 x 10³  +  2.28 x 10⁴    =  9.93 x 10³  +  22.8 x 10³  =  32.73 x 10³   =      3.27 x 10⁴

or  9.93 x 10³  +  2.28 x 10⁴     becomes:

0.993 x 10⁴  +  2.28 x 10⁴     =   3.273 x 10⁴   =  3.27 x 10⁴

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5.56 x 10⁵⁵  -  3.44 x 10⁵⁵

Rule:  If exponents are the same, subtract the coefficients, keep exponent the same in the answer. 

5.56 x 10⁵⁵  -  3.44 x 10⁵⁵    =  2.12 x 10⁵⁵

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8.33 x 10⁹  -  2.24 x 10⁸

Rule:  Subtraction requires similar exponents like addition does.  Fix exponents by adjusting coefficients, then subtract.  Fix coefficients to 1.0 to 9.9 if  necessary.  

8.33 x 10⁹  -  2.24 x 10⁸  becomes:

8.33 x 10⁹  -  0.224 x 10⁹  = 8.106 x 10⁹  = 8.11 x 10⁹ with 3 SF

or

8.33 x 10⁹  -  2.24 x 10⁸  becomes:  83.3 10⁸  -  2.24 x 10⁸ = 81.06 x 10⁸  =  8.11 x 10⁹

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1.99 x 10³⁶  -  2.38 x 10³⁴

Rule:  make the exponents the same by adjusting the coefficients, then subtract.
Fix coefficients by adjusting exponents if necessary.  Watch for sigfigs always.  

1.99 x 10³⁶  -  2.38 x 10³⁴

becomes:   1.99 x 10³⁶  -  0.0238 x 10³⁶  =  1.9662 x 10³⁶  =  1.97 x 10³⁶

^or

1.99 x 10³⁶  -  2.38 x 10³⁴

becomes: 

199 x 10³⁴  -  2.38 x 10³⁴    =  196.62 x 10³⁴  =   1.97 x 10³⁶

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4.56 x 10⁵  X  3.21 x 10⁵

Rule:  multiply the coefficients, ADD the exponents the same.  
Adjust coefficients and always watch for SF.  

4.56 x 10⁵  X  3.21 x 10⁵     =    14.6376 x 10¹⁰   =  1.46 x 10¹¹

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8.33 x 10⁹  X  2.24 x 10³

Rule:  multiply the coefficients, ADD the exponents.  
Adjust coefficients and always watch for SF.  

8.33 x 10⁹  X  2.24 x 10³      =   18.6592 x 10¹²    =   1.87 x 10¹³

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Multiply#3

9.93 x 10³¹  X  4.26 x 10²³

Rule:  multiply the coefficients, ADD the exponents.  
Adjust coefficients and always watch for SF. 

9.93 x 10³¹  X  4.26 x 10²³   =  42.3018 x 10⁵⁴    =  4.23 x 10⁵⁵

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8.10 x 10⁷  ÷  2.11 x 10³

^{Rule:  divide the coefficients, subtract the exponents.  Watch for coefficients and sigfigs always.}

8.10 x 10⁷  ÷  2.11 x 10³   =   3.8388625 x 10⁴   =  3.84 x 10⁴

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Divide#2

3.33 x 10¹²  ÷  2.11 x 10³

Rule:  divide the coefficients, subtract the exponents.  Watch for coefficients and sigfigs always.

3.33 x 10¹²  ÷  2.11 x 10^{3  =}   1.57819 x 10⁹  =  1.58 x 10⁹

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Divide#3

8.33 x 10⁹  ÷  2.24 x 10³

Rule:  divide the coefficients, subtract the exponents.  Watch for coefficients and sigfigs always.

8.33 x 10⁹  ÷  2.24 x 10³        =  3.71875 x 10⁶  =  3.72 x 10⁶

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