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LI: To understand Estimation and Approximation

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". Significant Figures

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LI: To understand Estimation and Approximation

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  1. LI: To understand Estimation and Approximation SC: Round numbers to a given number of decimal places and significant figures.

  2. Decimal Places • 0,1,2,3 and 4 are on team "down" • 5,6,7,8 and 9 are on team "up" 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.

  3. 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

  4. 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

  5. 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.

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