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.
1500
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 in standard - form is $1500 + 2200=3700$.

Step2: Convert sum to scientific notation

To write $3700$ in scientific notation, we move the decimal point 3 places to the left. So $3700 = 3.7\times 10^{3}$.

Step3: Explain shortcut

When adding numbers in scientific notation with the same exponent, we add the coefficients. For $1.5\times 10^{3}+2.2\times 10^{3}$, we add the coefficients $1.5$ and $2.2$: $(1.5 + 2.2)\times 10^{3}=3.7\times 10^{3}$.

Answer:

a. $1.5\times 10^{3}=1500$, $2.2\times 10^{3}=2200$, sum is $3700$.
b. $3.7\times 10^{3}$
c. Add the coefficients ($1.5$ and $2.2$) since the exponents are the same, resulting in $(1.5 + 2.2)\times 10^{3}=3.7\times 10^{3}$.