Question

Unit 1: Scientific Notation Constructed Response Assignment
Number Properties. explanations, according to the Scientific Notation Constructed Response Assignment Rubric. Completely respond to all parts below. When you have finished, submit your completed assignment to the Unit 1: Scientific Notation Constructed Response Assignment folder in your Math OMS course.

The diameter of the average cell in the human body is 1 x 10-5 meters. The diameter of a grain of sand is about 2 x 10-4 meters. The diameter of a human hair is about 0.000025 meters.

Part A (2 points): What is the diameter of a human hair written in scientific notation?



Part B (2 points): How many times longer is the diameter of a grain of sand than the diameter of the average cell in the human body? Show your work.




Part C (2 points): Given that 1 meter = 1 x 109 nanometers, what is the diameter of the average cell in the human body, in nanometers? Show your work.




Part D (2 points): The smallest known bacteria are from the genus Mycoplasma and can measure as small as 300 nanometers in diameter. Given that 1 meter = 1 x 109 nanometers, what is the diameter of the smallest bacteria, in meters? Give your answer in scientific notation and show your work.

Answer 1

https://brainly.com/question/5027087

Let C, S and H be the diameters of cell, sand and hair


Diameter of a cell: $C=1 \cdot 10^{-5}m$

Diameter of a grain of sand: $S=2 \cdot10^{-4}m$

Part A:

$H=0.000025=2.5 \cdot 10^{-5}$ meters, because it takes 5 movements right of the decimal dot, until there is only one digit to its left.

Part B:

we are comparing $S=2 \cdot10^{-4} m$ to $C=1 \cdot10^{-5} m$ ,

$\frac{S}{C}= \frac{2 \cdot 10^{-4}}{1 \cdot 10^{-5}}=\frac{20 \cdot 10^{-5}}{1 \cdot 10^{-5}}=20$

thus S is 20 times larger than C

Part C

$1m=1 \cdot10^9nm$

thus,

$H=2.5 \cdot 10^{-5}m=2.5 \cdot 10^{-5} \cdot 1 \cdot 10^9nm=2.5 \cdot 10^{-5+9}=2.5\cdot10^4nm$

Part D.

$1m=1\cdot 10^9nm\\\\1nm=\displaystyle{ \frac{1m}{10^9}=1\cdot 10^{-9}m}$

thus 300 nm are written in meters as follows:

$300nm= 300\cdot 1\cdot 10^{-9}m=3\cdot 10^2 \cdot 10^{-9}m=3\cdot 10^{-7}m$