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

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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

Writing numbers in standard form - Part 2

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


Transcript

59760000 = 5976 × 〖10〗^4 = (5.976 × 〖10〗^3) × 〖10〗^4 = 5.976 × 〖10〗^3 × 〖10〗^4 Using 𝑎^𝑚 × 𝑎^𝑛 = 𝑎^(𝑚 + 𝑛) = 5.976 × 〖10〗^(3 + 4) = 5.976 × 〖10〗^7 528000000 = 528 × 〖10〗^6 = (5.28 × 〖10〗^2) × 〖10〗^6 = 5.28 × 〖10〗^2 × 〖10〗^6 Using 𝑎^𝑚 × 𝑎^𝑛 = 𝑎^(𝑚 + 𝑛) = 5.28 × 〖10〗^(2 + 6) = 5.28 × 〖10〗^8

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.