Indices and Index Notation Solutions Practice Questions 5

Indices and Index Notation Solutions: Practice Questions 5. 7 CHAPTER 05

05 1. (i) Practice Questions 5. 7 How many orders of magnitude are in the following numbers? 567, 230, 356 = 5⋅67230356 × 108 Since 5⋅6723 > 5 Order of magnitude = n + 1 1+8= =9

05 1. (ii) Practice Questions 5. 7 How many orders of magnitude are in the following numbers? 123, 456 = 1· 23456 × 105 Since 1· 23456 < 5 Order of magnitude = n =5

05 1. (iii) Practice Questions 5. 7 How many orders of magnitude are in the following numbers? 20, 987 = 2· 0987 × 104 Since 2⋅0987 < 5 Order of magnitude = n =4

05 1. (iv) Practice Questions 5. 7 How many orders of magnitude are in the following numbers? 0⋅000567 = 5⋅67 × 10 – 4 Since 5⋅67 > 5 Order of magnitude = n + 1 –=1+4

05 1. (v) Practice Questions 5. 7 How many orders of magnitude are in the following numbers? 0⋅00298 = 2⋅98 × 10 – 3 Since 2⋅98 < 5 Order of magnitude = n – =3

05 1. (vi) Practice Questions 5. 7 How many orders of magnitude are in the following numbers? 0⋅00000323 10 × 23⋅3 = 00000323⋅0 – 6 Since 3⋅23 < 5 Order of magnitude = n –=6

05 1. Practice Questions 5. 7 How many orders of magnitude are in the following numbers? (vii) 0⋅085 10 × 5⋅8 = 085⋅0 2– Since 8⋅5 > 5 Order of magnitude = n + 1 1 + 2– = 1– =

05 1. Practice Questions 5. 7 How many orders of magnitude are in the following numbers? (viii) 0· 0000076 = 7⋅6 × 10 – 6 Since 7⋅6 > 5 Order of magnitude = n + 1 – = 61 + – =5

05 1. (ix) Practice Questions 5. 7 How many orders of magnitude are in the following numbers? 116 = 1⋅16 × 102 Since 1⋅16 < 5 Order of magnitude = n =2

05 1. (x) Practice Questions 5. 7 How many orders of magnitude are in the following numbers? 89 89 = 8⋅9 × 101 Since 8⋅9 > 5 Order of magnitude = n + 1 =11 + =2

05 2. (i) Practice Questions 5. 7 Find the order of magnitude estimate for each of the following: The length of a virus is 2· 8 × 10− 3 m. 2⋅8 × 10– 3 Since 2· 8 < 5 Order of magnitude = n – =3

05 2. (ii) Practice Questions 5. 7 Find the order of magnitude estimate for each of the following: The number of atoms in 12 g of carbon is 6 × 1023 Since 6 > 5 Order of magnitude = n + 1 1 + 23 = =24

05 2. (iii) Practice Questions 5. 7 Find the order of magnitude estimate for each of the following: A google is 10100 = 1 × 10100 Since 1 < 5 Order of magnitude = n =100

05 2. (iv) Practice Questions 5. 7 Find the order of magnitude estimate for each of the following: The age of the universe is 14· 6 billion years. 14⋅6 billion = 14, 600, 000 = 1⋅46 × 1010 Since 1· 46 < 5 Order of magnitude = n =10

05 2. (v) Practice Questions 5. 7 Find the order of magnitude estimate for each of the following: The diameter of a human hair is 25 × 10 − 6 m. 10 × 25 10 × 5⋅2 = 6– 5– Since 2· 5 < 5 Order of magnitude = n 5– =

05 3. (i) Practice Questions 5. 7 The mass of an electron is 9· 11 × 10− 31 kg. The mass of a proton is 1· 67 × 10− 27 kg. What is the order of magnitude for both the mass of a proton and the mass of an electron? Electron Proton 9⋅11 × 10– 31 1⋅67 × 10– 27 Since 9· 11 > 5 Since 1· 67 < 5 Order of magnitude = n + 1 Order of magnitude = n 1 + − 31 = − =30 − =27

05 3. (ii) Practice Questions 5. 7 The mass of an electron is 9· 11 × 10− 31 kg. The mass of a proton is 1· 67 × 10− 27 kg. Find the order of magnitude comparison between the mass of a proton and the mass of an electron. Therefore, a proton is 3 orders of magnitude heavier than an electron.

05 3. (Ii) Practice Questions 5. 7 The mass of an electron is 9· 11 × 10− 31 kg. The mass of a proton is 1· 67 × 10− 27 kg. Find the order of magnitude comparison between the mass of a proton and the mass of an electron. Alternatively: Comparison = difference in order of magnitude of mass of Proton and Electron (30 –) – 27 – = 30 + 27 – = =3

05 4. (i) Practice Questions 5. 7 The population of the Earth in 2015 was 7, 324, 782, 225. The population of Ireland was 4, 635, 400. What is the order of magnitude for each population? Earth Ireland 7, 324, 782, 225 4, 635, 400 = 7⋅324782225 × 109 610 Since 7· 32… > 5 Since 4· 6354 < 5 Order of magnitude = n + 1 Order of magnitude = n =9 + 1 =6 =10 × 6354⋅4 =

05 4. (ii) Practice Questions 5. 7 The population of the Earth in 2015 was 7, 324, 782, 225. The population of Ireland was 4, 635, 400. Find the order of magnitude comparison for the population of Earth to the population of Ireland.

05 4. (ii) Practice Questions 5. 7 The population of the Earth in 2015 was 7, 324, 782, 225. The population of Ireland was 4, 635, 400. Find the order of magnitude comparison for the population of Earth to the population of Ireland. Alternatively: Comparison = difference in order of magnitude of population of Earth and Ireland 6 – 10 = =4

05 5. (i) Practice Questions 5. 7 Make an order of magnitude estimate for the following: Your age in hours. Age = 17 years = 17 × 365 × 24 = 148920 hours = 1⋅48920 × 105 Since 1· 4892 < 5 Order of magnitude = n =5

05 5. (ii) Practice Questions 5. 7 Make an order of magnitude estimate for the following: The number of breaths you take in a year, given an average breathing rate of 16 breaths per minute. Number of breaths in a year = 365 days × 24 hours × 60 minutes × 16 breaths per minute 8, 409, 600 = = 8⋅4096 × 106 Since 8· 4096 > 5 Order of magnitude = n + 1 =6+1 =7

05 5. (ii) Practice Questions 5. 7 Make an order of magnitude estimate for the following: The number of heartbeats in a lifetime, given an average pulse rate of 72 beats per minute and an average life expectancy of 80 years. Number of heartbeats in 80 years × 365 days × 24 hours × 60 minutes × 72 beats per minute = 3, 027, 456, 000 = 3⋅027456 × 109 Since 3· 02… < 5 Order of magnitude = n =9

Practice Questions 5. 7 05 6. (i) The area of Australia is 7· 692 million km 2. The area of Ireland is 84, 421 km 2. Find the order of magnitude comparison between the area of Australia and the area of Ireland. Australia Ireland 7⋅692 million 84, 421 = 7, 692, 000 = 8⋅4421 × 104 610 × 692⋅7 = Since 7· 692 > 5 Since 8· 4421 > 5 Order of magnitude = n + 1 =6+1 =4+1 =7 =5

Practice Questions 5. 7 05 6. (i) The area of Australia is 7· 692 million km 2. The area of Ireland is 84, 421 km 2. Find the order of magnitude comparison between the area of Australia and the area of Ireland.

Practice Questions 5. 7 05 6. (i) The area of Australia is 7· 692 million km 2. The area of Ireland is 84, 421 km 2. Find the order of magnitude comparison between the area of Australia and the area of Ireland. Alternatively: Comparison = difference in area of Australia and Ireland =7 – 5 =2

05 6. Practice Questions 5. 7 (ii) The population of Australia in 2013 was 23· 13 million. The population of Ireland in 2013 was 4· 595 million. Find the order of magnitude comparison between the population of Australia and the population of Ireland in 2013. Population of Australia Population of Ireland = 23⋅13 million 4⋅595 million = 23, 130, 000 4, 595, 000 = 2⋅313 × 107 4⋅595 × 106 Since 2· 313 < 5 Since 4· 595 < 5 Order of magnitude = n =7 =6

05 6. Practice Questions 5. 7 (ii) The population of Australia in 2013 was 23· 13 million. The population of Ireland in 2013 was 4· 595 million. Find the order of magnitude comparison between the population of Australia and the population of Ireland in 2013.

05 6. Practice Questions 5. 7 (ii) The population of Australia in 2013 was 23· 13 million. The population of Ireland in 2013 was 4· 595 million. Find the order of magnitude comparison between the population of Australia and the population of Ireland in 2013. Alternatively: Comparison = difference in order of magnitude of population of Australia and Ireland =7 – 6 =1