**Standard Form**

Here we will learn a form of writing numbers. We use the standard form to express very large and very small numbers e.g. 327,800, 000, or 0.000096. The standard form is written as a x 10^{n} where a is a number between 1 and 10 and n is a +ve or –ve integer.

Example 1

- The number 327800 000 = 3.278 x 100000000

= 3.278 x 10^{3}

This is its standard form, i.e. in the format a x 10^{n}, here *a* 3.278 and this lies between 1 and 10, and *n*=8

Sometimes very small numbers are also better understood if written in standard form.

Consider the number 0.000096 which is equal to 9.6/100000

i.e. 0.00096 = 9.6/100000 = 9.6 x 1/100000 = 9.6 x 1/10^{5 }= 9.6 x 10 ^{-5}.

This is its standard form. Here a = 9.6 which is between 0 and 10 and n= -5

Converting to natural form from Standard Form

2.79 x 10^{6}

i.e. 2.79 x 10^{6}

= 2.79 x 1000000

= 279000000

Note:

- Both
*a*and*n*can be positive or negative, *n*can be*0*,

iii. *a* can be whole number or decimal fraction,

- Any number can be expressed in its standard form, although it is usually more convenient to use the standard form for every large or very small numbers and write other numbers in their natural/ordinary forms.

**Expanded Form**

In this form, the place values are emphasized like in the abacus

e.g. 23 = (2 x 10) +3

469 = (4 x 100) + 6(10) + 9

= 4 x 10^{2 }+ 6 x 10 + 9

= 4 x 10^{2 }+ 6 x 10^{1} + 9 x 10^{0 }– the expanded form of writing the number 469.

**EXERCISES**

Lets see how much you’ve learnt, attach the following answers to the comment below

- Write in standard forms the number 363220 A. 3.6322 x 10
^{3}B. 3.6322 x 10^{5 }C. 3.6322 x 10^{4}D. 3.6322 x 10^{-5} - Write in standard forms the number 0.0000523 A. 523 x 10
^{-7 }B. 5.23 x 10^{-6}C. 5.23 x 10^{-7 }D. 523 x 10^{-6 } - Express in their natural form 7.3 x 10
^{3}A. 73000 B. 730000 C. 7300 D. 70003 - Express in their natural form 8.325 x 10
^{2}A. 8325000 B. 83250 C. 83250000 D. 832500 - Express this 7.992 x 10
^{-4 }in natural form A. 0007992 B 007992 C. 00007992 D. 07992