Question

Express the following numbers in standard form.
(i) 0.0000000000085
(ii) 0.00000000000942
(iii) 6020000000000000
(iv) 0.00000000837
(v) 31860000000

Answer 1

(i) 0.0000000000085
To convert this small number into the standard form we need to move the decimal to its right by 12 steps.
\(= \frac{85}{10000000000000}\)

\(= 8.5 × \frac{10}{10¹³}\)
\(= 8.5 × 10^{-13} × 10\)
\(= 8.5 × 10^{-12}\)
∴ The standard form of a given number is \(8.5 × 10^{-12}\)

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(ii) 0.00000000000942
\(= \frac{942}{100000000000000} \)

\(= 9.42 × \frac{10^2 }{ 10^{14}}\)
\(= 9.42 × 10^{−14} × 10^2\)
\(= 9.42 × 10^{−12}\)
∴ The standard form of a given number is \(9.42 × 10^{−12}\)

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(iii) 6020000000000000
= 6.02 × 10² × 10000000000000
= 6.02 × 10² × 10¹³
= 6.02 × 10¹⁵
∴ The standard form of the given number is 6.2 × 10¹⁵

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(iv) 0.00000000837
\(= \frac{837 }{ 100000000000}\)

\(= 8.37 × \frac{10^2 }{ 10^{11}}\)

= 8.37 × 10⁻¹¹×10²
= 8.37 × 10⁻⁹
∴ The standard form of a given number is 8.37 × 10⁻⁹

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(v) 31860000000
= 3.186 × 10³ × 10⁷
= 3.186 ×10¹⁰
∴ The standard form of the given number is 3.186 × 10¹⁰