Scientific Notations of Real Numbers and Logarithms

• Rule for writing a number in standard form:

Place a decimal point after the first digit from the left in the number. Next, count the number of digits in the number after the decimal point and remove all the zeroes, if any, which appear at the end of the number. This number of digits equals the exponent of 10 that has to be multiplied with the decimal.

For example, 2943 can be written is standard form as:

• When a number is written in standard form, its decimal part is greater than or equal to 1.0 and lesser than 10.0.
• Rule for identifying a number from its standard form:

First write the exponent of 10 as a number and then multiply it with the decimal part to obtain the required number.

For example, 9.005 × 10⁶ can be written in normal form as:

9.005 × 10⁶ = 9.005 × 1000000 = 9005000

• If a is any positive real number (except 1), …