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rr Approximation
r, and Estimation

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One way to approximate the exact value is by rounding - round up or
round down or to the nearest.

For example, consider the whole numbers 22,25 and27 .

20 21 22 23 24 25 26 27 28 29 30

22 is nearer to 20 than 30. thus it is rounded down to 20.

27 is closer to 30 and thus it is rounded up to 30.
As a general guide, 25, which is exactly halfway between 20 and 30,
is rounded up to 30.

Rounding decimals can also be done in the same way.

Rules for rounding:
1. Consider one digit to the right of the place value of rounding.
2.
(i) If this digit is > 5 (ii) If this digit is < 5
For rounding whole numbers
add 'l' to the digit in the place |
. the digit in the place value of
value of rounding I rounding remains unchanged
and
a replace the digit(s) to the right of the place value with 0
For rounding decimals
o add '1' to the digit in the place | ' the digit in the place value of
value of rounding rounding remains unchanged
and
. 'drop' the digit(s) to the right of the place value of rounding

CH,A,F3THF: 3 ] E4
::i, : i : i I ii.;r. l;l l-:i,..: r.-i :'i:::-.
. All non-zero digits are significant.
. A zero (or zeros) between non-zero digits is (are) significant.
. In a whole number, zeros after the last non-zero digit may or may
not be significant.
. In a decimal, zeros before the first non-zero digit are not signiflcant.
. In a decimal, zeros after the last non-zero digit are significant.

>'F EXAMPLE 1 ' -; i,t:;.r'rl :1,:rit:'::-ri:ii lil-ll

Correct each of the following numbers to the nearest 50.
(a) 22638
(b) 23sttz (c) s7 s67

}F"
(a)
SOLUTION
22650
I
''t,
For (a), 22 638 is closer to
22 650 than to 22 600. Likewise,

(b) 23s r00 for (b), 235 112 is closer to

235 100 than to 235 150; for (c),
(c) 57 550 +
57 567 is closer to 57 550 than

i to 57 600.

};" EXAMPLE 2 i,'r,r,;irjiri! r:r ,,.i

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Round 48 379 to the nearest
(a) thousand, (b) ten thousand.

}.}e SOLUTION
oig"'8' is the place value;
(a) 48 379 = 48 000 ,$
consider one digit to the right.
i.e. '3', which is less than 5, thus
'8'remains unchanged and all
the digits after'3'are replaced
with 0.

Digit '4' is the place value:

(b) 48 379 = 50 000
{ consider one digit to the right,
i.e. '8'. which is more than 5.
thus we add 1 to 4 and replace
i all the digits on the right with 0.

>.3 EXAMPLE 3 i,r llj:il{.i il:: ii:1, 'ari1 .'1, :il :1.1t;..i i r: i j,:'il:,'ili:l t.i
Round 6.3501 correct to
(a) I decimal place, (b) 3 decimal places.

}}= SOLUTION
(a) 6.3501= 6.4
f Digit '3' is the first decimall
consider one digit to its right, i.e.
'5', thus we add 1 to 3 and drop

i all the other decimals.

(b) 6.3501 = 6.350

f Digit '0'is the third decimal:
consider one digit to its right, i.e.
'1'. which is less than 5, thus '0'
I remains unchanged and the digit
1 is dropped.

!:5 Ct-jAPTEn 3
Round 107.0305 correct to
(a) 2 significant figures,
(b) 4 significant figures,
(c) 5 significant figures,
(d) 6 signiflcant figures.

>tr SOLUTION
(a) 110
(b) 107.0
(c) 107.03
(d) 107.031

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To estimate the value of the result of numbers in a calculation, the numbers

in our working should be rounded to one more significant figure than
that of the required result.

>"b EXAMPLE$1,.'t -. .,,. ,, ., ' i.r;',ii,-:r'tr'l-:f 11111rr:fr,,-:'r,'l,i:it;r't;l

Estimate the value of .,405 x 11.3 - 44.7 corect to 1 significant figure.

>F SOLUTION
Jros x tt .3 - 44.j
= Joo x 11- 45 / ./ Round all the numbers to 2

= 10x ll-45 significant figures.

=65 /'''t. Do not forget to check if your

answer is correct to 1 significant
-70 i is not,you mustround
flgure.If it
.i up/down once more.

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