Question

Choose the option with the proper number of sig figs

Answer 1

`\text{ 2 }*10^8`

Step-by-step explanation:
`\begin{gathered} \text{Given:} \\ \frac{9\text{ }*10^9}{4.5\text{ }*10^1} \end{gathered}`

let's break down the expression to get the final result:

`\begin{gathered} \frac{9\text{ }*10^9}{4.5\text{ }*10^1}\text{ = }(9)/(4.5)*\text{ }(10^9)/(10^1) \\ (9)/(4.5)\text{ = }\frac{9\text{ }*\text{ 10}}{4.5\text{ }*\text{ 10}}\text{ = }(90)/(45) \\ (9)/(4.5)\text{ = }2 \\ \\ (10^9)/(10^1)\colon\text{ when we divide exponents with same base, } \\ we\text{ take one of the base and combine the exponents by subtracting them:} \\ (10^9)/(10^1)=10^(9-1) \\ (10^9)/(10^1)=10^8 \end{gathered}`
`\begin{gathered} (9)/(4.5)*\text{ }(10^9)/(10^1)\text{ = 2 }*10^8 \\ \\ \text{when dividing decimals, }the\text{ least number of }significant\text{ }figures\text{ in the problem}, \\ \text{ }\det ermines\text{ the significant figures in the answer} \\ 9\text{ = 1 significant, 4.5 = 2 significant} \\ \text{The least significant is 1} \\ \\ \frac{9\text{ }*10^9}{4.5\text{ }*10^1}\text{ = 2 }*10^8 \end{gathered}`