**1. Express the following numbers in standard form.**

**(i) 0.0000000000085**

**Solution:**

= 0.0000000000085×(10^{12}/10^{12}) = 8.5 ×10^{-12}

**(ii) 0.00000000000942**

**Solution:**

= 0.00000000000942×(10^{12}/10^{12}) = 9.42×10^{-12}

**(iii) 6020000000000000**

**Solution:**

= 6020000000000000×(10^{15}/10^{15}) = 6.02×10^{15}

**(iv) 0.00000000837**

**Solution:**

= 0.00000000837×(10^{9}/10^{9}) = 8.37×10^{-9}

**(v) 31860000000**

**Solution:**

= 31860000000×(10^{10}/10^{10}) = 3.186×10^{10}

**2.Express the following numbers in usual form.**

**(i) 3.02×10 ^{-6}**

**Solution:**

= 3.02/10^{6} = 0 .00000302

**(ii) 4.5×10 ^{4}**

**Solution:**

= 4.5×10000 = 45000

**(iii)3×10 ^{-8}**

**Solution:**

= 3/10^{8} = 0.00000003

**(iv)1.0001×10 ^{9}**

**Solution:**

= 1000100000

**(v) 5.8×10 ^{12}**

**Solution:**

= 5.8×1000000000000 = 5800000000000

**(vi)3.61492×10 ^{6}**

**Solution:**

= 3.61492×1000000 = 3614920

**3. Express the number appearing in the following statements in standard form.**

**(i)1 micron is equal to 1/1000000 m.**

**Solution:**

1 micron = 1/1000000

= 1/10^{6}

= 1×10^{-6}

**(ii) Charge of an electron is 0.000, 000, 000, 000, 000, 000, 16 Coulomb.**

**Solution:**

= 0.00000000000000000016×1019/10^{19}

= 1.6×10^{-19} coulomb

**(iii) Size of bacteria is 0.0000005 m**

**Solution:**

= 5/10000000

= 5/10^{7} = 5×10^{-7} m

(**iv) Size of a plant cell is 0.00001275 m**

**Solution:**

= 0.00001275×10^{5}/10^{5}

= 1.275×10^{-5}m

**(v) Thickness of a thick paper is 0.07 mm**

**Solution:**

= 7/100 mm = 7/10^{2} = 7×10^{-2} mm

**4. In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack?**

**Solution:**

Thickness of one book = 20 mm

Thickness of 5 books = 20×5 = 100 mm

Thickness of one paper = 0.016 mm

Thickness of 5 papers = 0.016×5 = 0.08 mm

Total thickness of a stack = 100+0.08 = 100.08 mm

= 100.08×10^{2}/10^{2} mm

= 1.0008 x 10^{2} mm

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