Addition and Subtraction (Exponential Notation)

Exponential Notation

Addition and Subtraction

When adding or subtracting numbers in scientific notation, the exponents must be the same.

• Step 1 - add/subtract the decimal

• Step 2 – Bring down the given exponent on the 10

Multiple Choice

 $\left(5.6×10^8\right)−\left(3.24×10^8\right)$  

•  $8.84\times10^8$  

•  $2.44\times10^8$  

•  $2.36\times10^8$  

Multiple Choice

 $\left(1.95×10^{12}\right)+\left(8.02×10^{12}\right)$  

•  $9.97\times10^{12}$  

•  $7.93\times10^{12}$  

•  $6.07\times10^{12}$  

Multiple Choice

 $\left(8.9×10^{-8}\right)−\left(6.76×10^{-8}\right)$  

•  $2.73\times10^{-8}$  

•  $2.26\times10^{-8}$  

•  $2.14\times10^{-8}$  

Multiple Choice

 $\left(9.33×10^{-17}\right)+\left(3.63×10^{-17}\right)$  

•  $12.96\times10^{-17}$  

•  $1.296\times10^{-16}$  

•  $1.296\times10^{-18}$  

NOTE:

• When adding or subtracting numbers in scientific notation, the exponents must be the same.

• If they are different, you must move the decimal so that they will have the same exponent.

Adding/Subtracting when the Exponents are DIFFERENT

• Step 1 – Rewrite so the exponents are the same 

• Step 2 - add/subtract the decimal

• Step 3 – Bring down the given exponent on the 10

Adding/Subtracting when the Exponents are DIFFERENT

•  $\left(5.7×10^8\right)+\left(1.27×10^9\right)$ 

•  $\left(0.57\times10^9\right)+\left(1.27\times10^9\right)$  
  

•  $\left(0.57+1.27\right)=1.84$  

•  $1.84\times10^9$  

Adding/Subtracting when the Exponents are DIFFERENT

•  $\left(5.7×10^8\right)+\left(1.27×10^9\right)$ 

•  $\left(5.7\times10^8\right)+\left(12.7\times10^8\right)$  
  

•  $\left(5.7+12.7\right)=18.4$  

•  $18.4\times10^8$  

•  $1.84\times10^9$  

Multiple Choice

 $(4.23×10^3)–(9.56×10^2)$  

•  $32.74×10^2$  

•  $3.274×10^3$  

•  $3.274×10^2$  

Multiple Choice

 $\left(7.6×10^{-15}\right)−\left(4.91×10^{-16}\right)$  

•  $7.109\times10^{-15}$  

•  $7.109\times10^{-16}$  

•  $7109\times10^{-15}$  

Multiple Choice

 $\left(2.7×10^{10}\right)+\left(4.71×10^9\right)$  

•  $31.71\times10^9$  

•  $3.171\times10^9$  

•  $3.171\times10^{10}$  

Multiple Choice

 $\left(3.12×10^{14}\right)−\left(1.82×10^{12}\right)$  

•  $4.94\times10^{14}$  

•  $3.1018\times10^{14}$  

•  $1.3\times10^{14}$  

Multiple Choice

 $\left(4.97×10^5\right)+\left(5.21×10^3\right)$  

•  $10.18\times10^5$  

•  $5.221\times10^5$  

•  $5.0221\times10^5$