Writing numbers in standard form

Suppose we have two numbers

  59760000 & 528000000

How do we compare them?

Comparing them becomes difficult when the number are large.

So, we write both number in standard form

So, our two numbers are

  5.976 × 10 ⁷

  5.28 × 10 ⁸

        Higher Power

So,

  5.28 × 10 ⁸ > 5.976 × 10 ⁷

Here,

  Standard form is

So, in standard form

• We write number as power of 10
• There is only 1 digit before decimal point

Let’s take some more examples

28488 in standard form

  28488

= 2.8488 × 10 ⁴

8680 in standard form

8680 = 868 × 10 ¹

= 8.68 × 10 ² × 10 ¹

Usinga ^m × a ⁿ = a ^{m + n}

= 8.68 × 10 ^{2 + 1}

= 8.68 × 10 ³

92058 in standard form

  92058  

  = 9.2058 × 10 ⁴

35.89 in standard form

  35.89  

    = 3589/100

    = 3589 × 1/100

    = 3589 × 1/10 ²

    = (3.589 × 10 ³ ) × 1/10 ²

    = 3.589 × 10 ³ /10 ²

    = 3.589 × 10 ^{3 - 2}

    = 3.589 × 10 ¹      (Using  a ^m /a ⁿ  =  a ^{m - n} )

Write 2.008 in standard form

  2.008 

       = 2.008 × 10 ⁰

Write 0.00008 in standard form

  0.00008 

    = 8/100000

    = 8/10 ⁵

    = 8 × 10 ^-5

Write 0.0092 in standard form

  0.0092  

       = 92/10000

       = 92 × 1/10000

       = 9.2 × 10 × 1/10000

       = 9.2 × 1/1000

       = 9.2 × 1/10 ³

       = 9.2 × 10 ^-3