# Solved examples on Scientific Notation

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**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 10

^{8}

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 10

^{6}

**Solution :**

1,200,000 + 4.5 x 10

^{6}

= 1.2 x 10

^{6}+ 4.5 x 10

^{6}

= ( 1.2 + 4.5 ) 10

^{6}

= 5.7 x 10

^{6}

**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 10

^{7}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 10

^{9}

(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 10

^{7}

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 10

^{3}

As the exponent of 10 is positive so the decimal will shift to right

= 3.5 x 1000

= 3,500

**Exponents**

• Laws of Exponents

• Rational Exponents

• Integral Exponents

• Scientific notation

• Solved examples on Scientific Notation

• Solved Examples on Exponents

• Laws of Exponents

• Rational Exponents

• Integral Exponents

• Scientific notation

• Solved examples on Scientific Notation

• Solved Examples on Exponents

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