Compare Numbers in Standard Form

Standard (index) form is a shorthand way of writing a very large or a very small number.

It is written as a  number between 1 and 10 (but not equal to 10) multiplied by a power of 10, for example 2.94 × 10² or 4.8 × 10^-3.

In this activity, we will compare such numbers.

5830000 = 5.83 × 10⁶

11223392 = 1.1223392 × 10⁷

694000000 = 6.94 x 10⁸

These numbers are in increasing order because 10⁶  numbers are always smaller than 10⁷ numbers etc...

So,  5.83 × 10⁶ < 1.1223392 × 10⁷

Very small numbers can be written in standard form too and these will have negative powers.

0.00574 = 5.74 x 10^-3

0.00069 = 6.9 x 10^-4

0.000028 = 2.8 x 10^-5

These numbers are getting smaller because 10^-5  numbers are always smaller than 10^-4  numbers.

So,  2.8 x 10^-5 <  6.9 x 10^-4

Let's have a go at comparing some numbers in standard form.