HOMEWORK
CHAPTER 1
Chapter 1
Standard Form
· Rounding off positive numbers to a given number off significant figures
Significant figures refer to the digits of a number that is relevant to its precision.
The significant figures are as follows :
Example :
20 000 ( 1 significant figure )
36 000 ( 2 significant figures)
123 (3 significant figures )
9763 ( 4 significant figures )
For the decimal, all digits after the first significant figure are significant figures.
For example :
The significant figures of 0.007 389 are as follows :
0.007 3 8 9
First significant figure
Second significant figure
Third significant figure
Fourth significant figure
The significant figures of 0.058 000 are as follows :
0.05 8 0 0 0
First significant figure
Second significant figure
Third significant figure
Fourth significant figure
Fifth significant number
· Concept of standard form
Stating positive numbers in standard form
For numbers greater than or equal to 10 :
Example :
85 000 = 8.5 × 104
For numbers less than 1 :
Example :
0.000 439 = 4.39 × 10 -4
· Performing operations of addition, subtraction, multiplication and
division, stating the answers in standard form.
|
1) 8.4 × 10 3 + 2.7 × 10 3
|
2 ) 5.69 × 10 -5 - 4.94 × 10 -5 |
|
3 ) (8.7 × 10 -3 ) × ( 2.5 × 10 -5 )
|
4 ) (4.82 × 10 5 ) ÷ ( 6 × 10 -1 ) |
- State the number of significant figures for the numbers given below.
(a) 123
(b) 4202
(c) 500
(d) 5002
(e) 3.10
(f) 5.005
(g) 7.100
(h) 0.006
(i) 0.080
(j) 1.0010
(k) 4.0102
(l) 0.01001
- Round off each of the decimal numbers below according to the number of significant figures given in the bracket [ ].
(a) 0.6678 [2]
(b) 0.8759 [3]
(c) 0.0192 [1]
(d) 0.00708 [1]
(e) 0.00255 [2]
(f) 0.000 998 [1]
(g) 0.000 1005 [3]
(h) 0.0002008 [2]
(i) 0.00101001 [4]
(j) 0.0098989 [2]
3. Round off the given numbers below to 3 significant figures.
(k) 489 200
(l) 1085
(m) 3099
(n) 48 785
(o) 5 999
(p) 78.64
(q) 200.8
(r) 173.45
(s) 0.06927
(t) 0.1098
- Write each of the numbers below in standard form.
(a) 70 000
(b) 840 000
(c) 392 000 000
(d) 6 030 000 000
(e) 9 800 800 000
- Write each of the decimal numbers below in the standard form.
(a) 0.0002
(b) 0.0013
(c) 0.00506
(d) 0.0000034
(e) 0.0000000001
- Round off each of the numbers below according to the number of significant figures given in the bracket [ ].
(a) 38 745 [ 2]
(b) 40 968 [3]
(c) 8005 [3]
(d) 998 [1]
(e) 190 865 [4]
(f) 75 556 [3]
(g) 10 095 [2]
(h) 8 167 354 [3]
(i) 99 876 [2]
7. Change each of the numbers below to integer number.
(a) 3.2 × 104
(b) 1.53 × 108
(c) 2.04 × 1010
(d) 5.5 × 10-3
(e) 7.08 × 10-5
(f) 8.54 × 10-9
8. Solve each of the following sums and give your answer in standard form.
(a) 78 000 000 + 54 000 000
(b) 0.0000075 – 0.00000012
(c) 63 000 × 0.000015
(d) 3 930 000 ÷ 0.006
(e) 48 000
0.012
(f) 0.00000548
16
9. Round off each of the decimal numbers below according to the number of significant figures given in the bracket [ ].
(a) 39.68 [ 3]
(b) 46.75 [2]
(c) 8.095 [2]
(d) 108.98 [4]
(e) 539.635 [3]
(f) 75.099 [4]
(g) 2.945 [1]
(h) 18.888 [3]
(i) 25.255 [2]
(j) 608.08 [2]
