Question

adding and subtracting with scientific notation
leena needs to add the expressions written in scientific notation shown. use the example to answer a - c.
a. write each of the values in standard form and find the sum.
b. write the sum in scientific notation.
c. using your solution in b, how could leena have found the sum without writing the expressions in standard notation first?

Explanation:

Step1: Convert to standard form

$1.5\times 10^{3}=1500$ and $2.2\times 10^{3} = 2200$. Then the sum is $1500 + 2200=3700$.

Step2: Convert sum to scientific - notation

$3700 = 3.7\times 10^{3}$ since $3700=3.7\times1000$ and $1000 = 10^{3}$.

Step3: Explain non - standard form addition

Since the exponents of 10 are the same ($10^{3}$ in both numbers), we can add the coefficients ($1.5$ and $2.2$) directly. $1.5 + 2.2=3.7$, and then keep the common power of 10, which is $10^{3}$. So the sum is $3.7\times 10^{3}$.

Answer:

a. $1.5\times 10^{3}=1500$, $2.2\times 10^{3}=2200$, sum = 3700
b. $3.7\times 10^{3}$
c. Add the coefficients ($1.5 + 2.2 = 3.7$) and keep the common power of 10 ($10^{3}$).