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"
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.
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
... 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
 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)
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.
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