# 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"
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)
Significant Figures
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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.
```