Question

leveled practice in 7 and 8, perform the operation and express your answer in scientific notation.

1. (7×10^(-6))(7×10^(-6))
2. (3.76×10^5)+(7.44×10^5)
3. what is the value of n in the equation 1.9×10^7=(1×10^5)(1.9×10^n)?
4. find (-5.3×10^3)-(-8×10^2). use what you know about scientific notation to express your answer with a power of 10.
5. apply math models a scientist is determining the mass of 30,000 molecules of oxygen. a. how many significant digits should be in the solution? b. express the mass of 30,000 molecules of oxygen in scientific notation.
6. communicate and justify your friend says that the product of 4.8×10^8 and 2×10^3 is 9.6×10^24. is this answer correct? explain.
7. find (7.2×10^(-8))/(-3×10^(-2)). use what you know about scientific notation to express your answer with a power of 10.
8. a certain star is 4.3×10^2 light - years from earth. one light year is about 5.9×10^12 miles. how far from earth (in miles) is the star? express your answer in scientific notation.

Explanation:

7.

Step1: Multiply the coefficients

$(7\times7)\times(10^{- 6}\times10^{-6})$
$49\times(10^{-6}\times10^{-6})$

Step2: Use the rule of exponents $a^m\times a^n=a^{m + n}$

$49\times10^{-6+( - 6)}$
$49\times10^{-12}$

Step3: Rewrite in proper scientific - notation

Since $49 = 4.9\times10^1$, then $49\times10^{-12}=(4.9\times10^1)\times10^{-12}=4.9\times10^{-11}$

Step1: Add the coefficients

$(3.76 + 7.44)\times10^{5}$
$11.2\times10^{5}$

Step2: Rewrite in proper scientific - notation

Since $11.2=1.12\times10^1$, then $11.2\times10^{5}=(1.12\times10^1)\times10^{5}=1.12\times10^{6}$

Step1: Multiply the right - hand side

$(1\times10^{5})(1.9\times10^{n})=(1\times1.9)\times(10^{5}\times10^{n}) = 1.9\times10^{5 + n}$

Step2: Set equal to the left - hand side and solve for $n$

We have the equation $1.9\times10^{7}=1.9\times10^{5 + n}$. Since the coefficients are the same ($1.9$), the exponents must be equal. So $7=5 + n$.
Subtract 5 from both sides: $n=7 - 5=2$

Answer:

$4.9\times10^{-11}$

8.