01 real numbers - Converting Recurring Decimals into...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

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*...
View Full Document

This note was uploaded on 11/09/2011 for the course ECON 131 taught by Professor Dfsfddsf during the Spring '11 term at Université Paris 12 - Val-de-Marne.

Page1 / 4

01 real numbers - Converting Recurring Decimals into...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online