Logarithm Standard forms

Numbers such as 1000 can be converted to its power of ten in the form 10ⁿ where n can be term as the number of times the decimal point is shifted to the front of the first significant figure i.e. 10000 = 10⁴

Number                                                 Power of 10

• 10²
• 10¹
• 10⁰
  • 10^-3
  • 10^-1

Note: One tenth; one hundredth, etc are expressed as negative powers of 10 because the decimal point is shifted to the right while that of whole numbers are shifted to the left to be after the first significant figure.

A number in the form A x 10ⁿ, where A is a number between 1 and 10 i.e. 1<A<10 and n is an integer is said to be in standard form e.g. 3.835 x 10³ and 8.2 x 10^-5 are numbers in standard form.

Examples : Express the following in standard form

1. 7853
2. 382
3. 0.387
4. 0.00104

Solutions

1. 7853 = 7.853 x 10³
2. 382 = 3.82 x 10²
3. 0.387 = 3.87 x 10^-1
4. 0.00104 = 1.04 x 10^-3