A marathon race covers a distance of 42.195 km . What is this distance in meters? In miles?

Name: Problem 21, Chapter 1: Chemistry and Chemical Reactivity
Uploaded: 2020-06-03T11:56:04-08:00
Duration: 4 min 9 s
Channel: Pahk Thepchatri
Description: A marathon race covers a distance of 42.195 km . What is this distance in meters? In miles?

A marathon race covers a distance of 42.195 km . What is...

Key Concepts

Unit Conversion

Unit conversion is the process of changing a quantity expressed in one unit to another unit using conversion factors. It allows for measurements to be compared, combined, or understood in different contexts by maintaining the same quantity underlying the numbers. This fundamental concept is crucial across science, engineering, mathematics, and everyday applications.

Conversion Factor

A conversion factor is a ratio that expresses how many units of one measurement are equivalent to another unit. It is used to multiply a given measurement in order to transform it into a different unit, ensuring that the overall quantity remains consistent. Mastery of conversion factors is essential for successful unit conversions.

Metric System

The metric system is an internationally used decimal-based system of measurement that employs units such as meters, kilometers, and grams. It is characterized by its ease of conversion through powers of ten. Understanding the metric system is fundamental to performing unit conversions within the SI (International System of Units).

Imperial System

The imperial system is a measurement system commonly used in the United States and a few other regions that includes units like miles, feet, and inches. Unlike the metric system, conversions within the imperial system do not always follow a decimal structure, making familiarity with its conversion factors essential for accurate measurements.

Dimensional Analysis

Dimensional analysis is a method used to convert one unit to another by multiplying by conversion factors expressed as ratios. It ensures that the final outcome has the desired units by treating units algebraically. This systematic approach helps prevent errors and is widely applicable in physics, chemistry, engineering, and other sciences.

Transcript

00:01 One thing we should always remember when doing these conversion problems is to go ahead and identify the conversion ratios that we're going to need for the problem.

00:13 If we are given that there's 42 .195 kilometers of distance and we need to convert that into, meters sure that for every one kilometer there is about 1 ,000 meters so we can convert this into a multiplication problem where we try to divide out or cancel out common units so on the top we put 1 ,000 meters in this ratio and and then on the bottom, we're going to put the one kilometer.

01:08 What this allows us to do is to cancel out the kilometer since it's on top and bottom.

01:15 You know, kilometer over kilometer cancels out, leaving us being able to do a straight multiplication of 42 .195 against 1 ,000 meters.

01:35 The result is going to be 42 ,195 meters.

01:48 And you think about, does that even make sense? it should be that it's a much bigger number than it was previously, even though technically is the same amount of distance.

01:59 If you want to convert this into miles, again, we're going to find a conversion.

02:05 Conversion is going to be in this case.

02:07 Let me just look it up.

02:10 I'll do it this for every one mile.

02:15 You get 1 .6 meters.

02:18 Sorry, kilometers, 1 .6 kilometers.

02:22 All right.

02:24 So then we set it up the same way.

02:26 There's 42 .195 kilometers...