MATHEMATICS FORM ONE TOPIC 5-APPROXIMATIONS

MATHEMATICS FORM ONE TOPIC 5-APPROXIMATIONS

UNAWEZA JIPATIA NOTES ZETU KWA KUCHANGIA KIASI KIDOGO KABISA:PIGA SIMU:0787237719

APPROXIMATIONS

Is the process of rounding off a number in the given places in rounding makes numbers easier to deal with but at the same time reduces their accuracy.

The methods used for approximation or rounding off numbers are decimal places and significant figures.

ROUNDING OFF PROCEDURES

i) If the first neglected digit is greater or equal to 5 the digit occupying the place value will increase by 1 unit
ii) If the first neglectednumberis less than five, then the number occupying the required place value will remain unchanged.

ROUNDING OFF NUMBERS

Examples

Round off the followingnumbers to the nearest wholenumber.
a) 3425
b) 7.283
c) 6.674
d) 0.625
e) 36.12
f) 5446

Solutions

a) 3425≈ 3000
b) 7.283≈7
c) 6.674≈7
d) 0.625≈1
e) 36.12≈36
f) 5446≈5000
Round off the following to
a) 1 decimal place.
b) 2 decimal places.
c) 3 decimal places.
a) 23.7016
b) 0.0094

Solution

23.7016≈23.7 to 1 decimal place.
23.7016≈23.70 to 2 decimal place.
23.7016≈23.702 to 3 decimal places.
b) 0.0094
a) 0.0094≈0.0 to 1 decimal place.
b) 0.0094≈0.001 to 2 decimal place.
c) 0.0094≈0.009 to 3 decimal places.
Round off the followingnumberto the nearest
a) Wholenumber
b) Tenth
c) Hundredth
0.625
8.385

Solution

0.625
a) 0.625≈1 to wholenumbers
b) 0.625≈0.6 to tenth
c) 0.625≈0.63 to hundredths
8.385
a) 8.385≈8 to wholenumbers
b) 8.385≈8.4 to tenth
c) 8.385≈ 8.39 to hundredths

Example: Round off 84678 to

i) Tens

Solution

84678 = 84700

ii) Hundreds

Solution

84678 = 85000

iii) Thousands

Solution

84678 = 80000

Example: Round off 179999 correct to i) hundreds ii) Thousand iii) Tens iv )Ten thousands

Solution

i) 179999180000
ii) 180000

iii) 180000

iv) 180000

Significant Figures
The are the total number of digits in the given number including zero’s which are in between non-zero digits.
Note

i) Zero is a significant figure when is inbetweentwo non – zero digits
ii) When zero is an outcome of approximation (rounding off) where a 9 receives landbecomes ten, then zero of ten is a significant figure.

Examples: determine the number of significant figures in the following

i) 20896100

= There are six significant figures

ii) 0.00025060

= There are four significant figures

iii) 2.00008453

= There are nine significant figures

Examples: Re write following numbers correcting to the required of significant figures.

0.23678 to 3 significant figures

Solution

0.23678

∴= 0.24

2.09478 to 3 significant figures

Solution

2.09478

∴= 2.09

0.009994 to 2 significant figures

Solution

0.009994

∴= 0.010

0.00931225697 to 7significant figures

Solutions

0.00931225697

∴= 0.0093123