# Width measurements and conversions

## Homework Statement

The tiles are 2 thumbnail-thicknesses apart. A thumbnail has a thickness of about 0.90 mm. An inch is exactly 2.54 centimeters. One algae cell is 9.45 micrometers across.

a. How wide is the gap between tiles in centimeters?
b. How wide is the gap in inches
c. How many algae-thicknesses is the gap between tiles

## The Attempt at a Solution

First off, I just want to know if I did a and b correctly. To set up a, I took 0.90 mm x 2 to get 1.8 mm per gap. I then converted 1.8 millimeters in order to get to centimeters. I came up with 0.18 centimeters. For b, I just divided 0.18cm/2.54cm to get the answer in inches. As for c, I suppose I will just convert, what do you think about a and b so far?

LowlyPion
Homework Helper

## Homework Statement

a. How wide is the gap between tiles in centimeters?
b. How wide is the gap in inches
c. How many algae-thicknesses is the gap between tiles

## The Attempt at a Solution

First off, I just want to know if I did a and b correctly. To set up a, I took 0.90 mm x 2 to get 1.8 mm per gap. I then converted 1.8 millimeters in order to get to centimeters. I came up with 0.18 centimeters. For b, I just divided 0.18cm/2.54cm to get the answer in inches. As for c, I suppose I will just convert, what do you think about a and b so far?

A and B would be correct.

C is asking how many algae diameters across. That requires a unit-less ratio.

A and B would be correct.

C is asking how many algae diameters across. That requires a unit-less ratio.

Couldn't I just convert 9.45 micrometers to centimeters and divide by 0.18 cm to get the thickness between the gaps in terms of algae thicknesses?

LowlyPion
Homework Helper
Couldn't I just convert 9.45 micrometers to centimeters and divide by 0.18 cm to get the thickness between the gaps in terms of algae thicknesses?

The question asks for how many will fit across. You divide the algae width INTO the gap in the tile dimension. Of course you need to make sure your units are correct, so the gap distance should be in the same units as the algae width.

So I converted 0.18 centimeters to micrometers and got 1800 micrometers. So then, I just take 1800 micrometers divded by 9.45 micrometers to get how many will fit across? 1800/9.45. I came up with 190.476, but since I can only have two significant figures in my answer, it would be 190 algae cells. How does that sound?