Solved examples on Scientific Notation

In this section check some some solved examples on scientific notation

Convert the following numbers into scientific form.
1) The nearest star to the earth is 149,600,000 km away from the sun.
Solution :

Distance = 149,600,000

As there is no decimal, consider it after 5 zeroes,

Shift decimal to left and place it before 1 so the exponent of 10 will be positive.

The decimal shifted to 8 places.

Scientific notation = 1.496 x 108

2) 0.0000067

Solution :

0.0000067

As we have to shift the decimal to right before 7 so exponent of 10 will be negative. The decimal shifted to 6 places.

Scientific notation = 6.7 x 10-6

3) Solve : 1,200,000 + 4.5 x 106

Solution :
1,200,000 + 4.5 x 106

= 1.2 x 106 + 4.5 x 106

= ( 1.2 + 4.5 ) 106

= 5.7 x 106

Express the numbers appearing in the following statements in the scientific form.

i) Diameter of the Earth is 12,756,000 meters.
As there is no decimal so, consider the decimal after the number and shift the decimal to left.
= 1.2756 x 107 m.

(ii) Diameter of the Sun is 1,400,000,000 meters.
As there is no decimal so, consider the decimal after the number and shift the decimal to left.
= 1.4 x 109

(iii) The size of the bacteria is 0.0000085.
As there is decimal so,shift the decimal to right.
= 8.5 x 10-6

Express the following numbers in the standard form.

(i) 4.83 x 107
As the exponent of 10 is positive so the decimal will shift to right
= 4.83 x 10,000,000
= 48,300,000

(ii) 3.5 x 103
As the exponent of 10 is positive so the decimal will shift to right
= 3.5 x 1000
= 3,500
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