{"id":234226,"date":"2025-06-14T02:36:55","date_gmt":"2025-06-14T02:36:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234226"},"modified":"2025-06-14T02:36:58","modified_gmt":"2025-06-14T02:36:58","slug":"unit-conversion-25-points-conversion-formula-1-km-1000-m-1-m-100-cm-1-mi-1-61-km-1-hr-3600-s-1-kg-1000-g","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/unit-conversion-25-points-conversion-formula-1-km-1000-m-1-m-100-cm-1-mi-1-61-km-1-hr-3600-s-1-kg-1000-g\/","title":{"rendered":"Unit conversion [25 points] Conversion formula: 1 km = 1000 m 1 m = 100 cm 1 mi = 1.61 km 1 hr = 3600 s 1 kg = 1000 g"},"content":{"rendered":"\n

Unit conversion [25 points] Conversion formula: 1 km = 1000 m 1 m = 100 cm 1 mi = 1.61 km 1 hr = 3600 s 1 kg = 1000 g a) [8 points] The speed of light in vacuum is 3.00 x 10
m\/s. What is this speed in kilometers per hour? b) [7 points] What is the speed of light in vacuum in miles per hour? c) [10 points] The density of aluminum is 2.70 g\/cm
. What is this density in kilograms per cubic meter?<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Problem 1: Unit Conversion [25 points]<\/h3>\n\n\n\n
\n\n\n\n

a) Speed of light in km\/hr<\/strong><\/h4>\n\n\n\n

The speed of light in vacuum is:3.00\u00d7108 m\/s3.00 \\times 10^8 \\ \\text{m\/s}3.00\u00d7108 m\/s<\/p>\n\n\n\n

Step 1: Convert meters to kilometers<\/strong>1 km=1000 m\u21d211000 km=1 m1 \\ \\text{km} = 1000 \\ \\text{m} \\Rightarrow \\frac{1}{1000} \\ \\text{km} = 1 \\ \\text{m}1 km=1000 m\u21d210001\u200b km=1 m3.00\u00d7108 m\/s=3.00\u00d71081000=3.00\u00d7105 km\/s3.00 \\times 10^8 \\ \\text{m\/s} = \\frac{3.00 \\times 10^8}{1000} = 3.00 \\times 10^5 \\ \\text{km\/s}3.00\u00d7108 m\/s=10003.00\u00d7108\u200b=3.00\u00d7105 km\/s<\/p>\n\n\n\n

Step 2: Convert seconds to hours<\/strong>1 hr=3600 s1 \\ \\text{hr} = 3600 \\ \\text{s}1 hr=3600 s3.00\u00d7105 km\/s\u00d73600 s\/hr=1.08\u00d7109 km\/hr3.00 \\times 10^5 \\ \\text{km\/s} \\times 3600 \\ \\text{s\/hr} = 1.08 \\times 10^9 \\ \\text{km\/hr}3.00\u00d7105 km\/s\u00d73600 s\/hr=1.08\u00d7109 km\/hr<\/p>\n\n\n\n

Answer (a):<\/strong>1.08\u00d7109 km\/hr\\boxed{1.08 \\times 10^9 \\ \\text{km\/hr}}1.08\u00d7109 km\/hr\u200b<\/p>\n\n\n\n

\n\n\n\n

b) Speed of light in mi\/hr<\/strong><\/h4>\n\n\n\n

1 mi=1.61 km1 \\ \\text{mi} = 1.61 \\ \\text{km}1 mi=1.61 km1.08\u00d7109 km\/hr\u00f71.61=6.71\u00d7108 mi\/hr1.08 \\times 10^9 \\ \\text{km\/hr} \\div 1.61 = 6.71 \\times 10^8 \\ \\text{mi\/hr}1.08\u00d7109 km\/hr\u00f71.61=6.71\u00d7108 mi\/hr<\/p>\n\n\n\n

Answer (b):<\/strong>6.71\u00d7108 mi\/hr\\boxed{6.71 \\times 10^8 \\ \\text{mi\/hr}}6.71\u00d7108 mi\/hr\u200b<\/p>\n\n\n\n

\n\n\n\n

c) Density of aluminum in kg\/m\u00b3<\/strong><\/h4>\n\n\n\n

Given:2.70 g\/cm32.70 \\ \\text{g\/cm}^32.70 g\/cm3<\/p>\n\n\n\n

Step 1: Convert grams to kilograms<\/strong>1 kg=1000 g\u21d22.70 g=2.701000=0.0027 kg1 \\ \\text{kg} = 1000 \\ \\text{g} \\Rightarrow 2.70 \\ \\text{g} = \\frac{2.70}{1000} = 0.0027 \\ \\text{kg}1 kg=1000 g\u21d22.70 g=10002.70\u200b=0.0027 kg<\/p>\n\n\n\n

Step 2: Convert cubic centimeters to cubic meters<\/strong>1 m=100 cm\u21d2(100 cm)3=106 cm31 \\ \\text{m} = 100 \\ \\text{cm} \\Rightarrow (100 \\ \\text{cm})^3 = 10^6 \\ \\text{cm}^31 m=100 cm\u21d2(100 cm)3=106 cm31 cm3=10\u22126 m31 \\ \\text{cm}^3 = 10^{-6} \\ \\text{m}^31 cm3=10\u22126 m3<\/p>\n\n\n\n

So:2.70 g\/cm3=0.0027 kg10\u22126 m3=2700 kg\/m32.70 \\ \\text{g\/cm}^3 = \\frac{0.0027 \\ \\text{kg}}{10^{-6} \\ \\text{m}^3} = 2700 \\ \\text{kg\/m}^32.70 g\/cm3=10\u22126 m30.0027 kg\u200b=2700 kg\/m3<\/p>\n\n\n\n

Answer (c):<\/strong>2700 kg\/m3\\boxed{2700 \\ \\text{kg\/m}^3}2700 kg\/m3\u200b<\/p>\n\n\n\n

\n\n\n\n

Explanation (300+ words)<\/h3>\n\n\n\n

Unit conversion is a fundamental skill in physics and engineering that allows measurements to be understood and compared across different systems. The process involves multiplying the original measurement by conversion factors that equal 1, ensuring that units cancel appropriately and yield the desired units.<\/p>\n\n\n\n

Part (a)<\/strong> involves converting the speed of light from meters per second (m\/s) to kilometers per hour (km\/hr). Since 1 kilometer equals 1000 meters, dividing by 1000 changes meters to kilometers. Then, multiplying by 3600 converts seconds to hours. This two-step process transforms the units from m\/s to km\/hr accurately. The result shows how extraordinarily fast light travels\u2014over a billion kilometers per hour.<\/p>\n\n\n\n

Part (b)<\/strong> requires converting the result from part (a) into miles per hour. Using the conversion factor 1 mile = 1.61 kilometers, the value in kilometers per hour is divided by 1.61 to yield miles per hour. This gives a better sense of scale for those familiar with imperial units and demonstrates the incredible speed of light in a different unit system.<\/p>\n\n\n\n

Part (c)<\/strong> focuses on converting a density measurement from grams per cubic centimeter (g\/cm\u00b3) to kilograms per cubic meter (kg\/m\u00b3), a common SI unit. To convert grams to kilograms, divide by 1000. To convert cubic centimeters to cubic meters, recognize that 1 m=100 cm1 \\text{ m} = 100 \\text{ cm}1 m=100 cm, so 1 m3=106 cm31 \\text{ m}^3 = 10^6 \\text{ cm}^31 m3=106 cm3. Therefore, each cm\u00b3 is 10\u2212610^{-6}10\u22126 m\u00b3, and the final conversion is accomplished by dividing kilograms by 10\u2212610^{-6}10\u22126, effectively multiplying the density by 10610^6106. This results in a commonly used density of 2700 kg\/m\u00b3 for aluminum.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Unit conversion [25 points] Conversion formula: 1 km = 1000 m 1 m = 100 cm 1 mi = 1.61 km 1 hr = 3600 s 1 kg = 1000 g a) [8 points] The speed of light in vacuum is 3.00 x 10m\/s. What is this speed in kilometers per hour? b) [7 points] […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-234226","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234226","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=234226"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234226\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234226"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234226"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}