What do you understand by scientific notation?

Difficulty: Hard

Scientific notation/Standard form:

In scientific notation, a number is expressed as some power of ten multiplied by a number between 1 and 10.

Examples:

1. The Moon is 384000000 meters away from the Earth. The distance of the moon from the Earth can also be expressed as 3.84 x 108 This saves writing down or interpreting large numbers of zeros.
2. A number 62750 can be expressed as 6.275 x 104. Similarly, the standard form of 0.00045 is 4.5 x 10-4

Quick Quiz

1. Name five prefixes most commonly used.

Ans:     (1) kilo (k) = 103      (2) centi(c)10-2        (3) milli(m) = 10-3

(4) micro (u) = 10-6        (5) mega (M) = 106

2.The Sun is one hundred and fifty million kilometres away from the Earth. Write this.

(a) as an ordinary whole number

(b) In scientific notation.

Ans:    The distance of Sun from the Earth = 150 million km

(A) as an ordinary whole number:

= 150 x 106km= 150 x 106 x 103m                                         1 million 106 1 kilo = 103

= 150000000000 m

(B) In scientific notation.

= 150 x 106 x 103

= 150 x 109

= 15 x 10 x 109

= 15 x 1010

= 15 ÷ 10 x 10 x 1010

=1.5 x 1011

=1.5 x 1011 m

3. Write the numbers given below in scientific notation.

1. 3000000000 ms-1 C.6400000 m
2. 0000000016 g       D. 0.0000548 s

Ans:

A. 3000000000 ms-1

= 3 x 1000000000 ms-1

= 3x 109 ms-1

B. 6400000 m

= 64 x 105m

= 6.4 x 10 x 105

= 6.4 x 106m

C. 0000000016 g

= 0.0000000016 ÷ 10000000000 g

= 16 x 10-10g

=1.6x 10x 10-10g

=1.6x10-9g

D. 0.0000548 s

= 0.0000548

=    0.0000548 ÷10000000

=    548 x 10-7

= 5.48 x 102 x 10-7

=5.48x 10-5

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