#### Large and Small Numbers

- To avoid confusion, when writing large numbers or small decimal fractions, group the digits in threes from the decimal point. E.g. 49 560 216 and 0.003 48.
- A number in standard form is written as a × 10
^{n}, where a is a number between 1 and 11 and n is a positive or negative integer. - The laws of indices are:
- y
^{a}× y^{b}= y^{a+b} - x
^{a}÷ x^{b}= x^{a-b} - x
^{0}= 1 - x
^{-a}=^{1}/x^{a} - (x
^{a})^{b}= x^{ab}

- y

__Examples__

__Examples__

- Express the following numbers in standard form:
- 60 000
- = 6 × 10 000
- = 6 × 10
^{4}

- 480 000 000
- = 4.8 × 100 000 000
- = 4.8 × 10
^{8}

- 60 000
- Express the following in ordinary form:
- 4.3 × 10
^{4}- = 4.3 × 10 000
- = 43 000

- 7.8 × 10
^{7}- = 7.8 × 10 000 000
- = 78 000 000

- 4.3 × 10
- Write the following as decimal fractions:
- 350 millionths
- = 1 millionth × 350
- = 0.000 001 × 350
- = 0.000 350
- = 0.000 35
**NOTE**: In a decimal fraction, it is not necessary to write any zeros after the last non-zero digit.

^{865}/_{100 000}- = 0.008 65
**NOTE**: There are five zeros in the denominator. The decimal fraction is obtained by moving the digits in the numerator five places to the right.

- 350 millionths
- Simplify the following:
- 10
^{4}× 10^{2}- = (10 × 10 × 10 × 10) × (10 × 10)
- = 10 × 10 × 10 × 10 × 10 × 10
- = 10
^{6} **OR more quickly, by adding indices:**10^{4}× 10^{2}= 10^{4+2}= 10^{6}

- 4c³ × 7c²
- = 4 × c × c × c × 7 × c × c
- = 4 × 7 × c × c × c × c × c
- = 28c
^{5} **OR more quickly, by adding indices:**4c³ × 7c² = 4 × 7 × c^{3+2}= 28c^{5}

- 10
- Simplify the following:
- 10
^{4}÷ 10^{2}- Using one of the laws of indices:
- = 10
^{4 – 2} - ∴ 10
^{4}÷ 10^{2 }= 10^{2}

- 4c³ ÷ 7c²
^{4}/_{7}× c^{3-2}- ∴ 4c³ ÷ 7c² =
^{4}/_{7}C

- 10