11 x1 t02 01 real numbers (2013)
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Transcript of 11 x1 t02 01 real numbers (2013)
![Page 1: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/1.jpg)
Real Numbers
![Page 2: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/2.jpg)
Real Numbers1. Prime FactorsEvery natural number can be written as a product of its prime factors.
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Real Numberse.g. 324
1. Prime FactorsEvery natural number can be written as a product of its prime factors.
![Page 4: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/4.jpg)
Real Numberse.g. 324 4 81
1. Prime FactorsEvery natural number can be written as a product of its prime factors.
![Page 5: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/5.jpg)
Real Numberse.g. 324 4 81
1. Prime FactorsEvery natural number can be written as a product of its prime factors.
2 42 3
![Page 6: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/6.jpg)
Real Numberse.g. 324 4 81
1. Prime FactorsEvery natural number can be written as a product of its prime factors.
2 42 3
2. Highest Common Factor (HCF)1) Write both numbers in terms of its prime factors
![Page 7: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/7.jpg)
Real Numberse.g. 324 4 81
1. Prime FactorsEvery natural number can be written as a product of its prime factors.
2 42 3
2. Highest Common Factor (HCF)1) Write both numbers in terms of its prime factors2) Take out the common factors
![Page 8: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/8.jpg)
Real Numberse.g. 324 4 81
1. Prime FactorsEvery natural number can be written as a product of its prime factors.
2 42 3
2. Highest Common Factor (HCF)1) Write both numbers in terms of its prime factors2) Take out the common factors
e.g. 1176 and 252
![Page 9: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/9.jpg)
Real Numberse.g. 324 4 81
1. Prime FactorsEvery natural number can be written as a product of its prime factors.
2 42 3
1176 6 196
2. Highest Common Factor (HCF)1) Write both numbers in terms of its prime factors2) Take out the common factors
e.g. 1176 and 252
3 2 49 4 3 23 2 7
![Page 10: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/10.jpg)
Real Numberse.g. 324 4 81
1. Prime FactorsEvery natural number can be written as a product of its prime factors.
2 42 3
1176 6 196
2. Highest Common Factor (HCF)1) Write both numbers in terms of its prime factors2) Take out the common factors
e.g. 1176 and 252
3 2 49 4 3 23 2 7
252 4 63 4 9 7
2 22 3 7
![Page 11: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/11.jpg)
Real Numberse.g. 324 4 81
1. Prime FactorsEvery natural number can be written as a product of its prime factors.
2 42 3
1176 6 196
2. Highest Common Factor (HCF)1) Write both numbers in terms of its prime factors2) Take out the common factors
e.g. 1176 and 252
3 2 49 4 3 23 2 7
252 4 63 4 9 7
2 22 3 7 22 3 7HCF
![Page 12: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/12.jpg)
Real Numberse.g. 324 4 81
1. Prime FactorsEvery natural number can be written as a product of its prime factors.
2 42 3
1176 6 196
2. Highest Common Factor (HCF)1) Write both numbers in terms of its prime factors2) Take out the common factors
e.g. 1176 and 252
3 2 49 4 3 23 2 7
252 4 63 4 9 7
2 22 3 7 22 3 7HCF
84
![Page 13: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/13.jpg)
Real Numberse.g. 324 4 81
1. Prime FactorsEvery natural number can be written as a product of its prime factors.
2 42 3
1176 6 196
2. Highest Common Factor (HCF)1) Write both numbers in terms of its prime factors2) Take out the common factors
e.g. 1176 and 252
3 2 49 4 3 23 2 7
252 4 63 4 9 7
2 22 3 7 22 3 7HCF
84When factorising, remove
the lowest power
![Page 14: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/14.jpg)
3. Lowest Common Multiple (LCM)
![Page 15: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/15.jpg)
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors
![Page 16: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/16.jpg)
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
![Page 17: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/17.jpg)
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
![Page 18: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/18.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3
![Page 19: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/19.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
![Page 20: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/20.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM
![Page 21: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/21.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM 240
![Page 22: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/22.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM 240
When creating a LCM, use the highest power
![Page 23: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/23.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM 240
When creating a LCM, use the highest power
4. Divisibility Tests
![Page 24: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/24.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM 240
When creating a LCM, use the highest power
4. Divisibility Tests
2: even number
![Page 25: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/25.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM 240
When creating a LCM, use the highest power
4. Divisibility Tests
2: even number3: digits add to a multiple of 3
![Page 26: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/26.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM 240
When creating a LCM, use the highest power
4. Divisibility Tests
2: even number3: digits add to a multiple of 3
4: last two digits are divisible by 4
![Page 27: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/27.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM 240
When creating a LCM, use the highest power
4. Divisibility Tests
2: even number3: digits add to a multiple of 3
4: last two digits are divisible by 45: ends in a 5 or 0
![Page 28: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/28.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM 240
When creating a LCM, use the highest power
4. Divisibility Tests
2: even number3: digits add to a multiple of 3
4: last two digits are divisible by 45: ends in a 5 or 06: divisible by 2 and 3
![Page 29: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/29.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM 240
When creating a LCM, use the highest power
4. Divisibility Tests
2: even number3: digits add to a multiple of 3
4: last two digits are divisible by 45: ends in a 5 or 06: divisible by 2 and 37: double the last digit and subtract from
the other digits, answer is divisible by 7
![Page 30: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/30.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM 240
When creating a LCM, use the highest power
4. Divisibility Tests
2: even number3: digits add to a multiple of 3
4: last two digits are divisible by 45: ends in a 5 or 06: divisible by 2 and 37: double the last digit and subtract from
the other digits, answer is divisible by 7
![Page 31: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/31.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM 240
When creating a LCM, use the highest power
4. Divisibility Tests
2: even number3: digits add to a multiple of 3
4: last two digits are divisible by 45: ends in a 5 or 06: divisible by 2 and 37: double the last digit and subtract from
the other digits, answer is divisible by 7
8: last three digits are divisible by 8
![Page 32: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/32.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM 240
When creating a LCM, use the highest power
4. Divisibility Tests
2: even number3: digits add to a multiple of 3
4: last two digits are divisible by 45: ends in a 5 or 06: divisible by 2 and 37: double the last digit and subtract from
the other digits, answer is divisible by 7
8: last three digits are divisible by 89: sum of the digits is divisible by 9
![Page 33: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/33.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM 240
When creating a LCM, use the highest power
4. Divisibility Tests
2: even number3: digits add to a multiple of 3
4: last two digits are divisible by 45: ends in a 5 or 06: divisible by 2 and 37: double the last digit and subtract from
the other digits, answer is divisible by 7
8: last three digits are divisible by 89: sum of the digits is divisible by 9
10: ends in a 0
![Page 34: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/34.jpg)
48 16 3
3. Lowest Common Multiple (LCM)1) Write both numbers in terms of its prime factors2) Write down all factors without repeating
e.g. 48 and 15
42 3 15 3 5
42 3 5LCM 240
When creating a LCM, use the highest power
4. Divisibility Tests
2: even number3: digits add to a multiple of 3
4: last two digits are divisible by 45: ends in a 5 or 06: divisible by 2 and 37: double the last digit and subtract from
the other digits, answer is divisible by 7
8: last three digits are divisible by 89: sum of the digits is divisible by 9
10: ends in a 011: sum of even positioned digits =
sum of odd positioned digits, or differ by a multiple of 11.
![Page 35: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/35.jpg)
Fractions & Decimals
![Page 36: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/36.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i
![Page 37: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/37.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
![Page 38: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/38.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
let 0.6x 0.666666x
![Page 39: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/39.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
let 0.6x 0.666666x
10 6.666666x
![Page 40: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/40.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
let 0.6x 0.666666x
10 6.666666x 9 6x
![Page 41: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/41.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
let 0.6x 0.666666x
10 6.666666x 9 6x
69
x 20.63
![Page 42: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/42.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
let 0.6x 0.666666x
10 6.666666x 9 6x
69
x 20.63
( ) 0.81ii 0.818181
![Page 43: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/43.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
let 0.6x 0.666666x
10 6.666666x 9 6x
69
x 20.63
( ) 0.81ii 0.818181 let 0.81x
0.818181x
![Page 44: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/44.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
let 0.6x 0.666666x
10 6.666666x 9 6x
69
x 20.63
( ) 0.81ii 0.818181 let 0.81x
0.818181x 100 81.818181x
![Page 45: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/45.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
let 0.6x 0.666666x
10 6.666666x 9 6x
69
x 20.63
( ) 0.81ii 0.818181 let 0.81x
0.818181x 100 81.818181x
99 81x
![Page 46: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/46.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
let 0.6x 0.666666x
10 6.666666x 9 6x
69
x 20.63
( ) 0.81ii 0.818181 let 0.81x
0.818181x 100 81.818181x
99 81x 8199
x 90.8111
![Page 47: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/47.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
let 0.6x 0.666666x
10 6.666666x 9 6x
69
x 20.63
( ) 0.81ii 0.818181 let 0.81x
0.818181x 100 81.818181x
99 81x 8199
x 90.8111
( ) 0.327iii 0.3272727
![Page 48: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/48.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
let 0.6x 0.666666x
10 6.666666x 9 6x
69
x 20.63
( ) 0.81ii 0.818181 let 0.81x
0.818181x 100 81.818181x
99 81x 8199
x 90.8111
( ) 0.327iii 0.3272727 let 0.327x
0.3272727x
![Page 49: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/49.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
let 0.6x 0.666666x
10 6.666666x 9 6x
69
x 20.63
( ) 0.81ii 0.818181 let 0.81x
0.818181x 100 81.818181x
99 81x 8199
x 90.8111
( ) 0.327iii 0.3272727 let 0.327x
0.3272727x 100 32.7272727x
![Page 50: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/50.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
let 0.6x 0.666666x
10 6.666666x 9 6x
69
x 20.63
( ) 0.81ii 0.818181 let 0.81x
0.818181x 100 81.818181x
99 81x 8199
x 90.8111
( ) 0.327iii 0.3272727 let 0.327x
0.3272727x 100 32.7272727x 99 32.4x
![Page 51: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/51.jpg)
Fractions & DecimalsConverting Recurring Decimals into Fractionse.g.( ) 0.6i 0.666666
let 0.6x 0.666666x
10 6.666666x 9 6x
69
x 20.63
( ) 0.81ii 0.818181 let 0.81x
0.818181x 100 81.818181x
99 81x 8199
x 90.8111
( ) 0.327iii 0.3272727 let 0.327x
0.3272727x 100 32.7272727x 99 32.4x
32.4 32499 990
x 180.32755
![Page 52: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/52.jpg)
Alternatively:e.g.( ) 0.6i
![Page 53: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/53.jpg)
Alternatively:e.g.( ) 0.6i 6
6 is recurring
![Page 54: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/54.jpg)
Alternatively:e.g.( ) 0.6i 6
923
6 is recurring1 number recurring,
use ‘9’
![Page 55: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/55.jpg)
Alternatively:e.g.( ) 0.6i 6
923
6 is recurring1 number recurring,
use ‘9’
( ) 0.81ii
![Page 56: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/56.jpg)
Alternatively:e.g.( ) 0.6i 6
923
6 is recurring1 number recurring,
use ‘9’
( ) 0.81ii 81
81 is recurring
![Page 57: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/57.jpg)
Alternatively:e.g.( ) 0.6i 6
923
6 is recurring1 number recurring,
use ‘9’
( ) 0.81ii 81
999
11
81 is recurring2 numbers recurring,
use ‘99’
![Page 58: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/58.jpg)
Alternatively:e.g.( ) 0.6i 6
923
6 is recurring1 number recurring,
use ‘9’
( ) 0.81ii 81
999
11
81 is recurring2 numbers recurring,
use ‘99’
( ) 0.7134iii
![Page 59: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/59.jpg)
Alternatively:e.g.( ) 0.6i 6
923
6 is recurring1 number recurring,
use ‘9’
( ) 0.81ii 81
999
11
81 is recurring2 numbers recurring,
use ‘99’
( ) 0.7134iii 71349999
23783333
![Page 60: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/60.jpg)
Alternatively:e.g.( ) 0.6i 6
923
6 is recurring1 number recurring,
use ‘9’
( ) 0.81ii 81
999
11
81 is recurring2 numbers recurring,
use ‘99’
( ) 0.7134iii 71349999
23783333
( ) 0.327iv
![Page 61: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/61.jpg)
Alternatively:e.g.( ) 0.6i 6
923
6 is recurring1 number recurring,
use ‘9’
( ) 0.81ii 81
999
11
81 is recurring2 numbers recurring,
use ‘99’
( ) 0.7134iii 71349999
23783333
( ) 0.327iv 324
327 – 3 ( subtract number not recurring)
![Page 62: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/62.jpg)
Alternatively:e.g.( ) 0.6i 6
923
6 is recurring1 number recurring,
use ‘9’
( ) 0.81ii 81
999
11
81 is recurring2 numbers recurring,
use ‘99’
( ) 0.7134iii 71349999
23783333
( ) 0.327iv 324
9901855
327 – 3 ( subtract number not recurring)2 numbers recurring, 1 not
use ‘990’
![Page 63: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/63.jpg)
Alternatively:e.g.( ) 0.6i 6
923
6 is recurring1 number recurring,
use ‘9’
( ) 0.81ii 81
999
11
81 is recurring2 numbers recurring,
use ‘99’
( ) 0.7134iii 71349999
23783333
( ) 0.327iv 324
9901855
327 – 3 ( subtract number not recurring)2 numbers recurring, 1 not
use ‘990’
( ) 0.1096v
![Page 64: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/64.jpg)
Alternatively:e.g.( ) 0.6i 6
923
6 is recurring1 number recurring,
use ‘9’
( ) 0.81ii 81
999
11
81 is recurring2 numbers recurring,
use ‘99’
( ) 0.7134iii 71349999
23783333
( ) 0.327iv 324
9901855
327 – 3 ( subtract number not recurring)2 numbers recurring, 1 not
use ‘990’
( ) 0.1096v 1086
1096 – 10
![Page 65: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/65.jpg)
Alternatively:e.g.( ) 0.6i 6
923
6 is recurring1 number recurring,
use ‘9’
( ) 0.81ii 81
999
11
81 is recurring2 numbers recurring,
use ‘99’
( ) 0.7134iii 71349999
23783333
( ) 0.327iv 324
9901855
327 – 3 ( subtract number not recurring)2 numbers recurring, 1 not
use ‘990’
( ) 0.1096v 1086
9900181
1650
1096 – 102 numbers recurring, 2 not
use ‘9900’
![Page 66: 11 x1 t02 01 real numbers (2013)](https://reader034.fdocuments.net/reader034/viewer/2022051017/55b601fdbb61eb210a8b46fb/html5/thumbnails/66.jpg)
Alternatively:e.g.( ) 0.6i 6
923
6 is recurring1 number recurring,
use ‘9’
( ) 0.81ii 81
999
11
81 is recurring2 numbers recurring,
use ‘99’
( ) 0.7134iii 71349999
23783333
( ) 0.327iv 324
9901855
327 – 3 ( subtract number not recurring)2 numbers recurring, 1 not
use ‘990’
( ) 0.1096v 1086
9900181
1650
1096 – 102 numbers recurring, 2 not
use ‘9900’
Exercise 2A;2adgj, 3bd, 4ac,5acegi, 6, 7cdg,8bdfhj, 9, 10bd,11ac, 12, 13*,
14*