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
}

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