Standard Form

Standard Form

Standard form helps us to write very large or very small numbers in an easily readable manner.

The standard form is of the format A x 10ⁿ, where A is a decimal between 1 and 10, n is an integer.

40000 = 4 x 10000 = 4 x 10⁴

42300 = 4.23 x 10000 = 4.23 x 10⁴

0.0423 = 4.23/100 = 4.23 x 10^-2

0.0000423 = 4.23/100000 = 4.23 x 10^-5

4 x 62 = 248 = 2.48 x 10²

(4 x 10²)² = 4² x (10²)² = 16 x 10⁴ = 1.6 x 10⁵

3 x (4 x 10²) = 12 x 10² = 1.2 x 10³

(6.2 x 10^-3)² = 6.2² x (10^-3)² = 38.44 x 10^-6 = 3.844 x 10^-5

Standard Form – Addition & Subtraction

To add or subtract numbers in standard form (A x 10ⁿ), n must be equal.

4.23 x 10⁴ + 8.71 x 10⁴

= (4.23 + 8.71) x 10⁴

= 12.94 x 10⁴

= 1.294 x 10⁵

3.71 x 10⁵ – 4.23 x 10⁴

Since n is not equal, adjust the decimal part (A) to make n equal.

= 3.71 x 10⁵ – 0.423 x 10⁵

= (3.71 – 0.423) x 10⁵

= 3.287 x 10⁵

Standard Form – Multiplication & Division

(7 × 10³) x (4 × 10²)

= 7 × 4 x 10³ x 10²

= 28 x 10⁵ because 10³ x 10² = 10³⁺² = 10⁵

= 2.8 x 10⁶ , adjusted to standard form.

(7.2 × 10⁴) x (4.8 × 10³) ÷ (2.4 × 10⁵)

= (7.2 × 4.8 ÷ 2.4) x (10⁴ x 10³ ÷ 10⁵)

= 14.4 x 10²

= 1.44 x 10³, adjusted to standard form.

Questions

1. Given that a= 5 x 10³ and b = 4 x 10² , find the value of the following in standard form : (i) a + b (ii) a - b (iii) ab (iv) a³

2. Mass of a micro item is 2.4 x 10^-32 kilograms. Express mass of 25 such items in grams, giving your answers in Standard Form.

3. Arrange the following is Ascending order : 212.4 x 10⁵ , 2.4 x 10⁶ , 2.412 x 10⁵ , 2.4 x 10^-3