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01 real numbers - Converting Recurring Decimals into...

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Real Numbers e.g. 324 4 81 = × 1. Prime Factors Every natural number can be written as a product of its prime factors. 2 4 2 3 = × 1176 6 196 = × 2. Highest Common Factor (HCF) 1) Write both numbers in terms of its prime factors 2) Take out the common factors e.g. 1176 and 252 3 2 49 4 = × × × 3 2 3 2 7 = × × 252 4 63 = × 4 9 7 = × × 2 2 2 3 7 = × × 2 2 3 7 HCF = × × 84 = When factorising, remove the lowest power
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48 16 3 = × 3. Lowest Common Multiple (LCM) 1) Write both numbers in terms of its prime factors 2) Write down all factors without repeating e.g. 48 and 15 4 2 3 = × 15 3 5 = × 4 2 3 5 LCM = × × 240 = When creating a LCM, use the highest power 4. Divisibility Tests 2: even number 3: digits add to a multiple of 3 4: last two digits are divisible by 4 5: ends in a 5 or 0 6: divisible by 2 and 3 7: double the last digit and subtract from the other digits, answer is divisible by 7 8: last three digits are divisible by 8 9: sum of the digits is divisible by 9 10: ends in a 0 11: sum of even positioned digits = sum of odd positioned digits, or differ by a multiple of 11.
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Fractions & Decimals Converting Recurring Decimals into Fractions
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Unformatted text preview: Converting Recurring Decimals into Fractions e.g.( ) 0.6 i & 0.666666 = K let 0.6 x = & 0.666666 x = K 10 6.666666 x = K 9 6 x = 6 9 x = 2 0.6 3 ∴ = & ( ) 0.81 ii & & 0.818181 = K let 0.81 x = & & 0.818181 x = K 100 81.818181 x = K 99 81 x = 81 99 x = 9 0.81 11 ∴ = & & ( ) 0.327 iii & & 0.3272727 = K let 0.327 x = & & 0.3272727 x = K 100 32.7272727 x = K 99 32.4 x = 32.4 324 99 990 x = = 18 0.327 55 ∴ = & & Alternatively: e.g.( ) 0.6 i & 6 = 9 2 3 = 6 is recurring 1 number recurring, use ‘9’ ( ) 0.81 ii & & 81 = 99 9 11 = 81 is recurring 2 numbers recurring, use ‘99’ ( ) 0.7134 iii & & 7134 9999 = 2378 3333 = ( ) 0.327 iv & & 324 = 990 18 55 = 327 – 3 ( subtract number not recurring) 2 numbers recurring, 1 not use ‘990’ ( ) 0.1096 v & & 1086 = 9900 181 1650 = 1096 – 10 2 numbers recurring, 2 not use ‘9900’ Exercise 2A; 2adgj, 3bd, 4ac, 5acegi, 6, 7cdg, 8bdfhj, 9, 10bd, 11ac, 12, 13*, 14*...
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