Question

Express the following numbers in usual form. 
(i) 3.02×10⁻⁶
(ii) 4.5×10⁴
(iii) 3×10⁻⁸
(iv) 1.0001×10⁹
(v) 5.8×10¹²
(vi) 3.61492×10⁶

Answer 1

(i) 3.02 ×10⁻⁶
To express a smaller number (with negative powers of 10) in its standard form, move the decimal point to the left by a number of places equal to the power of 10.
3.02 × 10⁻⁶ = 3.02/1000000
∴ its usual form is 0.00000302

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(ii) 4.5 × 10⁴
To represent a large number (with positive powers of 10) in its standard form, shift the decimal to the right by the number of places corresponding to the power of 10.
4.5 × 10⁴ = 45000
Thus, the usual form is 45000

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(iii) 3 × 10⁻⁸ = 0.00000003 [Shifting the decimal 8 places to the left.]

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(iv) 1.0001 × 10⁹ = 1000100000 [Shifting the decimal 9 places to the right.]

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(v) 5.8 × 10¹² = 5800000000000 [Shifting the decimal 12 places to the right.]

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(vi) 3.61492 × 10⁶ = 3614920 [Shifting the decimal 6 places to the right.]