Question

1. what is the value of n in the equation 1.9×10^7=(1×10^5)(1.9×10^n)? 11) 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? mass of one molecule of oxygen = 5.3×10^(-23) gra b. express the mass of 30,000 molecules of oxygen in scientific notation. 13. find (7.2×10^(-8))/(-3×10^(-2)). use what you know about scientific notation to express your answer with a power of 10.

Explanation:

9.

Step1: Simplify the right - hand side

First, multiply the non - exponential parts and the exponential parts separately. $(1\times10^{5})(1.9\times10^{n})=(1\times1.9)\times(10^{5}\times10^{n}) = 1.9\times10^{5 + n}$.

Step2: Solve for n

Set the right - hand side equal to the left - hand side: $1.9\times10^{7}=1.9\times10^{5 + n}$. Since the non - exponential parts are equal ($1.9 = 1.9$), we can set the exponents equal: $7=5 + n$.

Step3: Isolate n

Subtract 5 from both sides of the equation: $n=7 - 5$.

a.

The number 30000 has 1 significant digit (when written without a decimal point, trailing zeros are not significant), and the mass of one oxygen molecule $5.3\times10^{-23}$ has 2 significant digits. When multiplying or dividing, the result should have the least number of significant digits among the values used in the calculation. So, the solution should have 1 significant digit.

b.

The mass of one oxygen molecule is $m = 5.3\times10^{-23}$ grams. The mass of 30000 molecules is $M=30000\times5.3\times10^{-23}$. First, write 30000 in scientific notation: $30000 = 3\times10^{4}$. Then $M=(3\times10^{4})\times(5.3\times10^{-23})=(3\times5.3)\times(10^{4}\times10^{-23})=15.9\times10^{-19}$. Adjust to scientific notation: $M = 1.59\times10^{-18}$ grams. Since we need 1 significant digit, $M\approx1.6\times10^{-18}$ grams.

Step1: Divide the non - exponential parts

Divide 7.2 by - 3: $\frac{7.2}{-3}=-2.4$.

Step2: Divide the exponential parts

Use the rule $\frac{10^{a}}{10^{b}}=10^{a - b}$. So, $\frac{10^{-8}}{10^{-2}}=10^{-8-(-2)}=10^{-6}$.

Step3: Combine the results

Multiply the results from step 1 and step 2: $(-2.4)\times10^{-6}$.

Answer:

$n = 2$

11.