a. the diameter of the sun is approximately 1.391×10⁶ kilometres. the diameter of earth is approximately 12…

a. the diameter of the sun is approximately 1.391×10⁶ kilometres. the diameter of earth is approximately 12 742 kilometres. approximately how many earths could fit along the diameter of the sun?\nb. one water molecule weighs approximately 2.989×10⁻²⁶ kilograms. how many water molecules are there in lake ontario, which contains approximately 1.64×10¹⁵ kilograms of water?\nc. diatoms are a group of microalgae found in oceans, waterways, and soil. they are a primary source of food in the sea. one type of diatom measures 0.07 millimetres in length. how many diatoms would be needed to stretch along 1200 kilometres of shoreline?

a. the diameter of the sun is approximately 1.391×10⁶ kilometres. the diameter of earth is approximately 12 742 kilometres. approximately how many earths could fit along the diameter of the sun?\nb. one water molecule weighs approximately 2.989×10⁻²⁶ kilograms. how many water molecules are there in lake ontario, which contains approximately 1.64×10¹⁵ kilograms of water?\nc. diatoms are a group of microalgae found in oceans, waterways, and soil. they are a primary source of food in the sea. one type of diatom measures 0.07 millimetres in length. how many diatoms would be needed to stretch along 1200 kilometres of shoreline?

Answer

Explanation:

Step1: Convert Earth's diameter to scientific - notation

The diameter of Earth is $12742 = 1.2742\times10^{4}$ km. To find how many Earths could fit along the diameter of the sun, divide the sun's diameter by Earth's diameter. Let $n_1$ be the number of Earths. Then $n_1=\frac{1.391\times 10^{6}}{1.2742\times 10^{4}}$. Using the rule $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we have $n_1=\frac{1.391}{1.2742}\times10^{6 - 4}\approx1.092\times10^{2}=109.2\approx109$.

Step2: Find the number of water - molecules

Let $n_2$ be the number of water molecules in Lake Ontario. Given the weight of one water molecule is $2.989\times 10^{-26}$ kg and the weight of water in Lake Ontario is $1.64\times 10^{15}$ kg. Then $n_2=\frac{1.64\times 10^{15}}{2.989\times 10^{-26}}$. Using the rule $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we get $n_2=\frac{1.64}{2.989}\times10^{15-(-26)}\approx0.5487\times10^{41}=5.487\times 10^{40}$.

Step3: Convert units and find the number of diatoms

First, convert 1200 km to mm. Since $1$ km = $10^{6}$ mm, then $1200$ km=$1200\times10^{6}=1.2\times 10^{9}$ mm. Let $n_3$ be the number of diatoms. The length of one diatom is $0.07$ mm. Then $n_3=\frac{1.2\times 10^{9}}{0.07}=\frac{1.2\times 10^{9}}{7\times 10^{-2}}$. Using the rule $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we have $n_3=\frac{1.2}{7}\times10^{9-(-2)}\approx0.1714\times10^{11}=1.714\times 10^{10}$.

Answer:

a. Approximately 109 Earths could fit along the diameter of the sun. b. There are approximately $5.487\times 10^{40}$ water molecules in Lake Ontario. c. Approximately $1.714\times 10^{10}$ diatoms would be needed to stretch along 1200 km of shoreline.