NCERT Solutions for Class 8 Maths - Exponents and Powers - 2

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Exercise 10.2

Q1. Express the following numbers in standard form.
(i) 0.0000000000085
Sol: This number is 8.5 followed by 11 decimal places to the left, so in standard form, it is:
8.5 × 1 0 ^{− 12}

(ii) 0.00000000000942
Sol: This number is 9.42 followed by 11 decimal places to the left, so in standard form, it is:
9.42 × 1 0 ^{− 12} 

(iii) 6020000000000000
Sol: This number is 6.02 followed by 15 places to the right, so in standard form, it is: 6.02 × 10 ¹⁵

(iv) 0.00000000837
Sol: This number is 8.37 followed by 9 decimal places to the left, so in standard form, it is: 8.37 × 10 ^{− 9}

(v) 31860000000
Sol: This number is 3.186 followed by 10 places to the right, so in standard form, it is:
3.186 × 1 0¹⁰ 

Q2. Express the following numbers in usual form.
(i) 3.02×10⁻⁶
Sol: Shift the decimal point 6 places to the left:
0.00000302

(ii) 4.5 * 104
Sol: Shift the decimal point 4 places to the right:
45,000

(iii) 3 * 10–8
Sol: Shift the decimal point 8 places to the left:
0.00000003

(iv) 1.0001 * 109
Sol: Shift the decimal point 9 places to the right:
1,000,100,000

(v) 5.8 * 1012
Sol: Shift the decimal point 12 places to the right:
5,800,000,000,000

(vi) 3.61492 * 106
Sol: Shift the decimal point 6 places to the right: 
3,614,920

Q3. Express the number appearing in the following statements in standard form.
(i) 1 micron is equal to
Sol: This can be written as:
1×10⁻⁶m

(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.
Sol: This is:
1.6×10 ⁻¹⁹ coulomb

(iii) Size of a bacteria is 0.0000005 m.
Sol: This can be expressed as:
5×10 ⁻⁷ m

(iv) Size of a plant cell is 0.00001275 m.
Sol: This is:1.275×10 ⁻⁵ m

(v) Thickness of a thick paper is 0.07 mm.
Sol: To express this in meters and in standard form (considering 1 mm = 0.001 m 1 mm=0.001 m):
0.07 mm=0.07×0.001 m=7×10 ⁻² m

Q4. 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?
Sol: To find the total thickness of the stack, we need to sum the thicknesses of all the books and paper sheets.
Books Each book has a thickness of 20 mm. For 5 books, the total thickness is:
5 × 20 mm = 100 mm
Paper Sheets
Each paper sheet has a thickness of 0.016 mm. For 5 paper sheets, the total thickness is:
5×0.016mm=0.08mm
Total Thickness
Adding the thicknesses of the books and paper sheets together gives the total thickness of the stack:
100mm+0.08mm=100.08mm
Therefore, the total thickness of the stack is 100.08 mm.