Page 124 - Mathematics_Form_Two

Logarithms

4. For the numbers which are between 1 Example 6�3
and less than 10, the exponent of 10 is
0. Simplify each of the following expressions
5. In multiplication of numbers in and write the answers in standard form:
standard form, the exponents are (a) (7 × 10 ) (8 × 10 )
4
2
added, while in division the exponents (b) (7 × 10 )(8 × 10 )
(7 10READING ONLY
–4
–2
Mathematics for Secondary Schools Example 6�1 (a) ( 7 10 = = (7 8 56 10 )(8 10 ) (10 6 2 4 )  10 4 )
are subtracted.
Solution
2
Write each of the following numbers in
standard form:
(a) 230000000
(b) 245
=
(c) 0.00045
= 5.6 10 10 5.6 10  7 6
Solution
(a) 230000000 = 2.3 × 100000000 Therefore,
= 2.3 × 10 8 (7 × 10 ) (8 × 10 ) = 5.6 × 10 .
4
7
2
(b) 245 2.45 100 2.45 10=  =  2 2 4 2 4 6
−
(c) 0.00045 4.5 0.0001 4.5 10=  =  − 4 (b) (7 10 − )(8 10 − ) 7 8 10=  −  10 = 56 10 −
FOR ONLINE
−
4
= 4.5 10× − 4 − 2 )(8 10 − 4 ) 7 8 10=  − 2  10 = 56 10 − 6
(7 10 − 2 )(8 10 − 4 ) 7 8 10=  − 2 10 − 4 = 56 10 − 6
Example 6�2 = 5.6 10 1  10 − 6

= 5.6 10 − 5
Express each of the following numbers
in ordinary decimals numerals: Therefore,
(a) 4.8 10 3 (7 × 10 ) (8 × 10 ) = 5.6 × 10 .
–2
–4
–5
(b) 3.5 10 − 6
(c) 1.4 × 10 – 4
Example 6�4
Solution Evaluate each of the following
3
(a) 4.8 × 10 = 4.8 × 1000 expressions, giving the answers in
= 4800 standard form:
(b) 3.5×10 = 3.5 × 0.000001 8
−6
(a) 4 10
= 0.0000035 5 10 5

(c) 1.4×10 = 1.4 × 0.0001 (b)
−4
= 0.00014

118
Student's Book Form Two

11/10/2024 20:12:46
MATHEMATIC F2 v5.indd 118 11/10/2024 20:12:46
MATHEMATIC F2 v5.indd 118