Question

in 1 - 3, find the sum or difference. write your answers in scientific notation.

1. (6.2×10^8)+(2.3×10^8)
2. (9×10^ - 3)-(4×10^ - 3)
3. (1.9×10^ - 5)+(5.42×10^ - 5)
4. natasha needs to find the sum of 8.65×10^4 and 43,000.

a. set up the problem by writing both numbers in scientific notation. then, find the sum.
b. what do you notice about the sum, and how can you make sure it is written correctly in scientific notation?

Explanation:

Step1: Solve problem 1

We have $(6.2\times 10^{8})+(2.3\times 10^{8})$. Since the exponents are the same, we add the coefficients: $(6.2 + 2.3)\times10^{8}=8.5\times 10^{8}$.

Step2: Solve problem 2

For $(9\times 10^{-3})-(4\times 10^{-3})$, with the same exponents, we subtract the coefficients: $(9 - 4)\times10^{-3}=5\times 10^{-3}$.

Step3: Solve problem 3

For $(1.9\times 10^{-5})+(5.42\times 10^{-5})$, as the exponents are equal, we add the coefficients: $(1.9+5.42)\times 10^{-5}=7.32\times 10^{-5}$.

Step4: Solve problem 4 - part a

First, write $43000$ in scientific - notation. $43000 = 4.3\times 10^{4}$. Now find the sum of $8.65\times 10^{4}$ and $4.3\times 10^{4}$. Add the coefficients: $(8.65 + 4.3)\times10^{4}=12.95\times 10^{4}$. But in scientific notation, the coefficient should be between $1$ and $10$. So, $12.95\times 10^{4}=1.295\times 10^{5}$.

Step5: Solve problem 4 - part b

In scientific notation, the coefficient $a$ must satisfy $1\leq a<10$. In the initial sum of problem 4 part a, $12.95\times 10^{4}$ was not in correct scientific notation because $12.95>10$. We move the decimal point one place to the left and increase the exponent of $10$ by $1$ to get $1.295\times 10^{5}$.

Answer:

1. $8.5\times 10^{8}$
2. $5\times 10^{-3}$
3. $7.32\times 10^{-5}$
4. a. $1.295\times 10^{5}$

b. The coefficient in scientific notation must be between 1 and 10. If it is not, we adjust the decimal - point position and the exponent of 10 accordingly.