INDEX NOTATION
54÷56
5-2
1/2 x 1/2 x 1/2 x 1/2
(1/2)4
Round 0.007436 to 3 significant figures.
0.00744
Convert 0.00067 into standard form.
6.7 × 10⁻⁴
A scientist estimates that the mass of a dust particle is 5 × 10⁻⁹ g. If there are 3 × 10⁵ such particles in a room, what is their total mass in standard form?
(5×10-9)×(3×105)=15×10-4=1.5×10-3 g
t3 x m6 x t4 x m7
t7m13
(-2,1/4)3 in repeated multiplication
-2,1/4 x -2,1/4 x -2,1/4
0.0005281, round it to 2 significant figures.
Rounded to 2 SF: 5.3 × 10⁻⁴
Express 4,500,000 in standard form.
4.5 × 10⁶
Two numbers are given in standard form: A = 4 × 10⁶ and B = 2 × 10³. Without converting to ordinary numbers, determine the ratio A:B in its simplest form.
4x106/2x103=4/2x106-3=2x103
25y2z3 x 15yz2
375y3z5
2.5 x 2.5 x 2.5 in index form
(2.5)3
How many significant figures are there in 3.0450 × 10⁵?
5 significant figures
Calculate (3 × 10⁵) × (2 × 10³) and express the answer in standard form.
(3×2)×(105×103)=6×108
Ali claims that (2⁵ × 2³) ÷ 2² = 2⁶. Analyze his answer and determine if he is correct. If not, correct his mistake.
(25×23)÷22=2(5+3)÷22=28−2=26
Since the final result is 2⁶, Ali’s claim is actually correct.
272(4)
278
-16384 [base of -4]
(-4)7
The mass of a planet is given as 6.378 × 10²⁴ kg. Round this to 4 significant figures.
6.378 × 10²⁴ kg (Already in 4 SF!)
Simplify (8 × 10⁷) ÷ (4 × 10²) and express the answer in standard form.
(8÷4)×(107÷102)=2×105
Create a real-life scenario where the laws of indices are needed to simplify a problem, and solve it using index notation.
A lab has (8 × 10⁴)² bacteria at the start. The bacteria grow at a rate of 10² times every hour. How many bacteria will there be after 3 hours?
(8×104)2×102×3=82×108×106=64×1014=6.4×1015 bacteria
41/3 x 502/3 x 105/3
103
(2y3)5=2y15 True or False, if false what is the true answer
False, (32y15)
Calculate (3.42 × 10²) × (2.1 × 10³) and give the answer in correct SF.
(3.42×2.1)×(102×103)=7.182×105
Rounded to 2 significant figures (smallest SF from given numbers): =7.2×105
Solve (2 × 10⁻³) + (3 × 10⁻³) and express the answer in standard form.
(2+3)×10-3=5×10-3
You are designing a microscopic circuit board where each transistor is 3 × 10⁻⁷ m in width. If a circuit line consists of 2 × 10² such transistors in a row, what is the total length of the circuit line in standard form?
(3×10-7)×(2×102)=6×10-5 m