Writing a number in scientific notation

Definition

Scientific notation is written in the form: a x 10^n with 1 <= a < 10 (a has a single non-zero digit before the decimal point) and n a relative integer (positive, negative, or zero).

3-step method

1. Place the decimal point right after the first non-zero digit of the number.
2. Count how many places the decimal point was moved: this gives the absolute value of the exponent n.
3. Determine the sign of n: if the starting number is large (>= 10), n is positive; if the starting number is small (< 1), n is negative.

Examples

• 45000 -> we write 4.5 then count 4 moves to the left -> 4.5 x 10^4
• 0.00072 -> we write 7.2 then count 4 moves to the right -> 7.2 x 10^-4
• 300 -> 3 x 10^2
• 8 -> 8 x 10^0 (special case, zero exponent)

Converting back to decimal notation

For the reverse operation, the decimal point is moved in the direction indicated by the exponent. Example: 6.1 x 10^5 = 610000

Classic pitfall

A common mistake is writing 45 x 10^3 instead of 4.5 x 10^4. This is not mathematically wrong (45 x 10^3 = 45000), but it is not correct scientific notation because 45 is not between 1 and 10. Always check that 1 <= a < 10.