AMDG S1
CLASS NOTES
SIGNIFICANT
FIGURES
A digit or a figure is SIGNIFICANT if it gives an idea
of (i)
Quantity or
(ii)
Accuracy
Examples 1
A.
23400 has 3
significant figures
B.
5056 has 4
significant figures
C.
0.034 has 2
significant figures
D.
12.50 has 4
significant figures
E.
104.30600 has 8
significant figures
F.
0.04050 has 4
significant figures
Examples 2
A.
Round the
following to 1 significant figure (sig fig)
(i) 2650 3000
(ii)
72 400 70 000
(iii)
0.058 0.06
(iv)
0.00745 0.007
B.
Round the
following to 2 sig figs
(i) 956 960
(ii)
75 398 75 000
(iii)
1.567 1.6
(iv)
0.04897 0.049
(v)
0.07999 0.080 This is a tricky one!
Remember: Our answer must be
very close to the question in size.
TRY NOT TO MAKE THE FOLLOWING MISTAKE:
36 700 to 2 sig figs DOES NOT EQUAL 37. The correct answer is 37 000.
Scientific
Notation
Scientists often have to use
very large and very small numbers. To save writing all numbers in full, they
use a system called scientific notation or
standard form.
To write is Scientific
notation:
1.
Write down the
significant figures only
2.
Put the decimal
point after the first figure
3.
write ‘× 10’
4.
Give the 10 an
index (power) which tells you how many places to move the decimal point to get
the normal number. It also tells you the direction in which to move the decimal
point
Ie. 3
means 3 places right
-4
means 4 places left
The number in front must be between 1
and 10
Examples 1
A.
Write the
following in the normal way (normal form):
(i) 4.8 × 104 = 48 000
(ii) 7.56
× 106 = 7 560 000
(iii) 1.2 × 103 = 1 200
B.
Write the
following in the normal way:
(i)
7.4 × 10-3
= 0.0074
(ii)
8.56 × 10-4
= 0.000856
(iii)
1.0 × 10-2 = 0.01
Examples 2
A.
Express these
numbers in scientific notation:
(i) 27 000
= 2.7 × 104
(ii)
834 = 8.34 × 102
(iii)
7 560 = 7.56 × 103
B.
Express these
numbers in scientific notation:
(i) 0.054
= 5.4 × 10-2
(ii)
0.76 = 7.6 × 10-1
(iii)
0.000345 = 3.45 × 10-4