{"id":81038,"date":"2022-06-09T19:32:25","date_gmt":"2022-06-09T14:02:25","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=81038"},"modified":"2022-05-10T14:14:40","modified_gmt":"2022-05-10T08:44:40","slug":"eureka-math-grade-8-module-1-lesson-10","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-8-module-1-lesson-10\/","title":{"rendered":"Eureka Math Grade 8 Module 1 Lesson 10 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 8th Grade Module 1 Lesson 10 Answer Key<\/h2>\n

Eureka Math Grade 8 Module 1 Lesson 10 Exercise Answer Key<\/h3>\n

Exercise 1.
\nThe speed of light is 300,000,000 meters per second. The sun is approximately 1.5\u00d71011<\/sup> meters from Earth. How many seconds does it take for sunlight to reach Earth?
\nAnswer:
\n300 000 000=3\u00d7108<\/sup>
\n\\(\\frac{1.5 \\times 10^{11}}{3 \\times 10^{8}}\\) = \\(\\frac{1.5}{3}\\)\u00d7\\(\\frac{10^{11}}{10^{8}}\\)
\n=0.5\u00d7103<\/sup>
\n=0.5\u00d710\u00d7102<\/sup>
\n=5\u00d7102<\/sup>
\nIt takes 500 seconds for sunlight to reach Earth.<\/p>\n

Exercise 2.
\nThe mass of the moon is about 7.3\u00d71022<\/sup> kg. It would take approximately 26,000,000 moons to equal the mass of the sun. Determine the mass of the sun.
\nAnswer:
\n26 000 000=2.6\u00d7107<\/sup>
\n(2.6\u00d7 107<\/sup>)(7.3\u00d71022<\/sup>)=(2.6\u00d77.3)(107<\/sup>\u00d71022<\/sup>)
\n=18.98\u00d71029<\/sup>
\n=1.898\u00d710\u00d71029<\/sup>
\n=1.898\u00d71030<\/sup>
\nThe mass of the sun is 1.898\u00d71030<\/sup> kg.<\/p>\n

Exercise 3.
\nThe mass of Earth is 5.9\u00d71024<\/sup> kg. The mass of Pluto is 13,000,000,000,000,000,000,000 kg. Compared to Pluto, how much greater is Earth\u2019s mass than Pluto\u2019s mass?
\nAnswer:
\n13 000 000 000 000 000 000 000=1.3\u00d71022<\/sup>
\n5.9\u00d71024<\/sup>-1.3\u00d71022<\/sup>=(5.9\u00d7102<\/sup>)\u00d71022<\/sup>-1.3\u00d71022<\/sup>
\n=(590-1.3)\u00d71022<\/sup>
\n=588.7\u00d71022<\/sup>
\n=5.887\u00d7102<\/sup>\u00d71022<\/sup>
\n=5.887\u00d71024<\/sup>
\nThe mass of Earth is 5.887\u00d71024<\/sup> kg greater than the mass of Pluto.<\/p>\n

Exercise 4.
\nUsing the information in Exercises 2 and 3, find the combined mass of the moon, Earth, and Pluto.
\nAnswer:
\n7.3\u00d71022<\/sup>+1.3\u00d71022<\/sup>+5.9\u00d71024<\/sup>=(7.3\u00d71022<\/sup>+1.3\u00d71022<\/sup>)+5.9\u00d71024<\/sup>
\n=8.6\u00d71022<\/sup>+5.9\u00d71024<\/sup>
\n=(8.6+590)\u00d71022<\/sup>
\n=598.6\u00d71022<\/sup>
\n=5.986\u00d7102<\/sup>\u00d71022<\/sup>
\n=5.986\u00d71024<\/sup>
\nThe combined mass of the moon, Earth, and Pluto is 5.986\u00d71024<\/sup> kg.<\/p>\n

Exercise 5.
\nHow many combined moon, Earth, and Pluto masses (i.e., the answer to Exercise 4) are needed to equal the mass of the sun (i.e., the answer to Exercise 2)?
\nAnswer:
\n\\(\\frac{1.898 \\times 10^{30}}{5.986 \\times 10^{24}}\\) = \\(\\frac{1.898}{5.986}\\) \u00d7 \\(\\frac{10^{30}}{10^{24}}\\)
\n=0.3170\u2026\u00d7106<\/sup>
\n\u22480.32\u00d7106<\/sup>
\n=0.32\u00d710\u00d7105<\/sup>
\n=3.2\u00d7105<\/sup>
\nIt would take 3.2\u00d7105<\/sup> combined masses of the moon, Earth, and Pluto to equal the mass of the sun.<\/p>\n

Eureka Math Grade 8 Module 1 Lesson 10 Problem Set Answer Key<\/h3>\n

Have students practice operations with numbers written in scientific notation and standard notation.<\/p>\n

Question 1.
\nThe sun produces 3.8\u00d7102<\/sup>7 joules of energy per second. How much energy is produced in a year? (Note: a year is approximately 31,000,000 seconds).
\nAnswer:
\n31 000 000=3.1\u00d7107<\/sup>
\n(3.8\u00d71027<\/sup>)(3.1\u00d7107<\/sup>)=(3.8\u00d73.1)(1027<\/sup>\u00d7107<\/sup>)
\n=11.78\u00d71034<\/sup>
\n=1.178\u00d710\u00d71034<\/sup>
\n=1.178\u00d71035<\/sup>
\nThe sun produces 1.178\u00d71035<\/sup> joules of energy in a year.<\/p>\n

Question 2.
\nOn average, Mercury is about 57,000,000 km from the sun, whereas Neptune is about 4.5\u00d7109<\/sup> km from the sun. What is the difference between Mercury\u2019s and Neptune\u2019s distances from the sun?
\nAnswer:
\n57 000 000=5.7\u00d7107<\/sup>
\n4.5\u00d7109<\/sup>-5.7\u00d7107<\/sup>=(4.5\u00d7102<\/sup>)\u00d7107<\/sup>-5.7\u00d7107<\/sup>
\n=450\u00d7107<\/sup>-5.7\u00d7107<\/sup>
\n=(450-5.7)\u00d7107<\/sup>
\n=444.3\u00d7107<\/sup>
\n=4.443\u00d7102<\/sup>\u00d7107<\/sup>
\n=4.443\u00d7109<\/sup>
\nThe difference in the distance of Mercury and Neptune from the sun is 4.443\u00d7109<\/sup> km.<\/p>\n

Question 3.
\nThe mass of Earth is approximately 5.9\u00d71024<\/sup> kg, and the mass of Venus is approximately 4.9\u00d71024<\/sup> kg.
\na. Find their combined mass.
\nAnswer:
\n5.9\u00d71024<\/sup>+4.9\u00d71024<\/sup>=(5.9+4.9)\u00d71024<\/sup>
\n=10.8\u00d71024<\/sup>
\n=1.08\u00d710\u00d71024<\/sup>
\n=1.08\u00d71025<\/sup>
\nThe combined mass of Earth and Venus is 1.08\u00d71025<\/sup> kg.<\/p>\n

b. Given that the mass of the sun is approximately 1.9\u00d71030<\/sup> kg, how many Venuses and Earths would it take to equal the mass of the sun?
\nAnswer:
\n\\(\\frac{1.9 \\times 10^{30}}{1.08 \\times 10^{25}}\\)=\\(\\frac{1.9}{1.08} \\times \\frac{10^{30}}{10^{25}}\\)
\n=1.75925\u2026\u00d7105<\/sup>
\n\u22481.8\u00d7105<\/sup>
\nIt would take approximately 1.8\u00d7105<\/sup> Venuses and Earths to equal the mass of the sun.<\/p>\n

Eureka Math Grade 8 Module 1 Lesson 10 Exit Ticket Answer Key<\/h3>\n

Question 1.
\nThe speed of light is 3\u00d7108<\/sup> meters per second. The sun is approximately 230,000,000,000 meters from Mars. How many seconds does it take for sunlight to reach Mars?
\nAnswer:
\n230 000 000 000=2.3\u00d71011<\/sup>
\n\\(\\frac{2.3 \\times 10^{11}}{3 \\times 10^{8}}\\)=\\(\\frac{2.3}{3}\\)\u00d7\\(\\frac{10^{11}}{10^{8}}\\)
\n=0.7666\u2026\u00d7103<\/sup>
\n\u22480.77\u00d710\u00d7102<\/sup>
\n\u22487.7\u00d7102<\/sup>
\nIt takes approximately 770 seconds for sunlight to reach Mars.<\/p>\n

Question 2.
\nIf the sun is approximately 1.5\u00d71011<\/sup> meters from Earth, what is the approximate distance from Earth to Mars?
\nAnswer:
\n(2.3\u00d71011<\/sup>)-(1.5\u00d71011<\/sup>)=(2.3-1.5)\u00d71011<\/sup>
\n=0.8\u00d71011<\/sup>
\n=0.8\u00d710\u00d71010<\/sup>
\n=8\u00d71010<\/sup>
\nThe distance from Earth to Mars is 8\u00d71010<\/sup> meters.<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 8th Grade Module 1 Lesson 10 Answer Key Eureka Math Grade 8 Module 1 Lesson 10 Exercise Answer Key Exercise 1. The speed of light is 300,000,000 meters per second. The sun is approximately 1.5\u00d71011 meters from Earth. How many seconds does it take for sunlight to reach Earth? Answer: 300 … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/81038"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=81038"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/81038\/revisions"}],"predecessor-version":[{"id":137579,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/81038\/revisions\/137579"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=81038"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=81038"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=81038"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}