Page 125 - Mathematics_Form_Two

Logarithms

Solution (c) (6 10× 6 ) ( 2 10×− 4 ) (6 10×= 6 ) (0.02 10− × 6 )
4 10
(a) 4 10 8 =  8
5 10 5 5 10 5 (6 10× 6 ) ( 2 10×− 4 ) (6 10×= 6 ) (0.02 10− × 6 )

= 0.8 10 3 = (6 0.02) 10− × 6
 = 8 × 10 × 10
= 8.0 10  − -1 1 10 3 3 = 5.98 × 10 6
FOR ONLINE READING ONLY
= 8 × 10

= 8.0 10 2 2 (d) 3.14 10× − 2 − 4.03 10× − 3 = 3.14 10× − 2 − 0.403 10× − 2
Therefore, 4 10 8 = 8 × 10 . = 3.14−10 −0.403×10 −2
2
−2
4 848 5 5 = 4 848 10 - 5 -
5 10 10´
´
20 10 2 20 10 2 = (3.14−0.403)×10 −2
´
(b) Mathematics for Secondary Schools
´
= 242.4 10 7 - = 2.737 10× − 2
´
= 242.4 10 7 -
Exercise 6�1
= 2.424 10 ´ 2 10 - 7 1. Write each of the following numbers
´
´
= 2.424 10 5 - in standard form:
Therefore, 4 848 10´ - 5 = 2.424 10´ - 5 . (a) 31065 (b) 95.1
20 10´ 2 (c) 9999 (d) 6
1
Example 6�5 (e) (f) 69.03
100
Evaluate each of the following, giving (g) 253009115 (h) 5.41
the answers in standard form:
(i) 0.0004068 (j) 7.245
(a) 3 10× 4 + 4.32 10× 3
(k) 1985 (l) 0.000008
−3
(b) 5×10 +6×10 −5
(c) (6 10× 6 ) ( 2 10×− 4 ) (m) 3 (n) 30
4
(d) 3.14 10× − 2 − 4.03 10× − 3
(o) 463.18 (p) 265000
Solution 2. Write each of the following in
(a) 3 10 +4.32 10× 4 × 3 = 3 10× 4 + 0.432 10× 4 decimal numerals:

3 10 +4.32 10× 4 × 3 = 3 10× 4 + 0.432 10× 4 (a) 9.10 × 10 5
= (3 0.432) 10+ × 4 (b) 7.4 × 10 – 4

= 3.432 10× 4 (c) 3 × 10 0 4
(b) 5 10× − 3 + 6 10× − 5 = 5 10 +0.06 10× − 3 × − 3 (d) 26.5 × 10 4

5 10× − 3 + 6 10× − 5 = 5 10 +0.06 10× − 3 × − 3 (e) 2.74 × 10
–3
= (5 0.06) 10×+ − 3 (f) 4.2 × 10
(g) 3.68 × 10 3
= 5.06 10× − 3 (h) 8.67 × 10 –2

119
Student's Book Form Two

11/10/2024 20:12:48
MATHEMATIC F2 v5.indd 119 11/10/2024 20:12:48
MATHEMATIC F2 v5.indd 119