Standard Form

A number in standard form — also known as scientific notation — looks like this:

\[ a \times 10^n \]

Where a is a number between 1 and 9.

And n is the number of times a must be multiplied by ten to get back to the original number.

If n is negative, then a is divided by ten a total of n times.

Examples

Converting ordinary numbers (floating point) to Standard Form:

\[ 345000 = 3.45 \times 10^5 \]

\[ 0.0062 = 6.2 \times 10^{-3} \]

Converting from Standard Form back to ordinary numbers:

\[ 4.2 \times 10^3 = 4200 \]

\[ 7.5 \times 10^{-2} = 0.075 \]

What distance is travelled by an object which travels for 4 hours at a speed of \(5 \times 10^2\) km/h?

\[ \text{Distance} = \text{speed} \times \text{time} = (5 \times 10^2) \times 4 = 20 \times 10^2 = 2 \times 10^3 \text{ km} \]

The number must be between 1 and 9, otherwise it is Engineering Form:

\[ 0.25 \times 10^4 = 2.5 \times 10^3 \]