This document discusses standard form and significant figures. It defines significant figures as all non-zero digits plus zeros between non-zero digits and zeros at the end of a decimal. Standard form expresses numbers as a value multiplied by a power of 10, where the value is between 1 and 10 and the power is positive for values ≥ 10 and negative for values ≤ 1. The document provides examples of identifying significant figures, rounding numbers, converting between regular and standard form numbers, and vice versa.

1. Form 4
Chapter 1 : Standard Form

2. 1.1 Significant figure
 All zeros between non-zero digits are significant figures (s.f).
Eg: 2008 [4 s.f]
506.07 [5 s.f.]
 All zeros at the end of a decimal are s.f.
Eg: 2.60 [3 s.f.]
7.1000 [5 s.f.]
 All zeros at the end of a whole number are not s.f. unless stated otherwise.
Eg : 1000 [1 s.f.]
1000 [2 s.f.]
1000 [3 s.f.]
1000 [4 s.f.]
 Number < 1
All zeros on the left-hand side of a non-zero digit are not s.f.
Eg: 0.168 [3 s.f.]
0.00068 [2 s.f.]

3. Try this exercise :
 State the number of significant figures.
a) 438
b) 40308
c) 7.060
d) 0.000078
e) 0.508
Answer :
a) 3
b) 5
c) 4
d) 2
e) 3

4. 1.1 a : Rounding off numbers
Do the digits after x
lie before or after the
decimal point ?
Identify the digit (x) that is to be rounded off
No
x remains unchanged
Add 1 to x
Is the digit after x
greater than or equal
to 5 ?
Replace each digit with a zero.
Drop the digits.
Before
After
Yes

5. Example :
Eg 1 : Round off 57.63 to :
a) 3 significant figures.
b) 1 significant figure.
Answer :
a) 57.6
b) 60
Eg 2 : Round off 0.002035 to :
a) 3 significant figures.
b) 1 significant figure.
Answer : a) 0.00204
b) 0.002

6. 1.2 Standard Form
Numbers written in the form :
A × 10n
where 1 ≤ A ≤ 10 and n is an integer.
 n is positive for numbers ≥ 10
 n is negative for numbers ≤ 1

7. 1.2 a: Expressing positive numbers in standard form
 Express the following numbers in standard form.
a) 1688
b) 290000
c) 0.035
d) 0.000123
Answer:
a) 1.688 x 103
b) 2.9 x 105
c) 3.5 x 10
-2
d) 1.23 x 10- 4

8. 1.2b : Converting standard form to single numbers
 Convert the following numbers in standard form to a
single number.
a) 5.43 x 105
b) 6.493 x 10- 3
c) 1.2345 x 10- 3
Answer:
a) 543 000
b) 0.006493
c) 0.0012345