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LI: To understand Estimation and Approximation SC: Round numbers to a given number of decimal places and significant figures. Decimal Places 0,1,2,3 and 4 are on team "down" 5,6,7,8 and 9 are on team "up" Examples Because ... 3.1416 rounded to 2dp is 3.14 ... the next digit (1) is less than 5 1.2635 rounded to 1dp is 1.3 ... the next digit (6) is 5 or more 1.2635 rounded to 3 dp is 1.264 ... the next digit (5) is 5 or more Significant Figures To round "so many" significant digits, just count digits from left to right, and then round off from there. Note: if there are leading zeros (such as 0.006), don't count them because they are only there to show how small the number is. Examples Because ... 1.239 rounded to 3 significant digits is 1.24 ... the next digit (9) is 5 or more 134.9 rounded to 1 significant digit is 100 ... the next digit (3) is less than 5 0.0165 rounded to 2 significant digits is 0.017 ... the next digit (5) is 5 or more Tauranga City Tauranga is a growing and vibrant city of over 111,000 people. Our population has almost doubled in the last 20 years and by 2021 it is expected to reach 141,000. The city covers an area of 13,440 hectares. We have a ten year plan projecting the Council’s capital expenditure over the next decade to be around $1,103,450,000. On average, 60% of our expenditure each year is growth related. As at 30 June 2010 we had 50,026 rateable residential and commercial properties. Revenue received from rates in the 2009/10 year was $82.46 million. The total assets of the Council as at 30 June 2010 were $3.523 billion and total liabilities $397.5 million. Tauranga has a higher than average number of residents who identify themselves as Maori -16.1% compared to 14.7% nationally (source: 2006 Census). There are three main iwi that most Tauranga Maori residents are affiliated to – Ngaiterangi, Ngati Rangainui and Ngati Pukenga. Tauranga has a sub-tropical climate. The average temperature is 14.2C and the city enjoys about 2,400 hours of sunshine a year. Average rainfall is 1,349mm (1.349m) http://www.tauranga.govt.nz/about-tauranga-city.aspx Significant Figures The population of Auckland in 1991 was 885,571. What is this to the nearest 10? What is this to the nearest 100, 1000, 10000, 100000? Mt. Everest is 8854 m high. A particular book says it was 8900 m high. The book is right if it is given to the nearest 100 m. Which figures are significant? 8 and 9 What is the point of the zeros? placeholders Mount Cook is 3753.5 metres high. How would your rewrite this number if rounded to 2 significant figures? 3800 m Round it to the nearest 10m. 3750m How many sig. figs. does the number have now? 3 Significant Figures E.g. George uses 6.852cm of wood for his craft boat. Round this number to 3 sig. figs. 6.85cm There are 46.965grams of salt required for a science experiment. Round this number to 3 sig. figs. 47.0g 0.0504725 was the reading on a pressure monitor. Round this to 4 sig. figs. 0.05047 In Terenceville, 34592 people contracted a highly contagious flu. Round this number to 2 sig. figs. 35,000 To round to a number of significant figures: Count the required number of figures from the first non-zero figure. Omit the following figures. If the first figure omitted is 5 or greater, increase the last figure by 1.