Express the following numbers in standard form:
(i) $6020000000000000$
(ii) $0.00000000000942$
(iii) $0.00000000085$
(iv) $846 \times 10^{7}$
(v) $3759 \times 10^{-4}$
(vi) $0.00072984$
(vii) $0.000437 \times 10^4$
(viii) $4 \div 100000$

To do :

We have to express each of the given numbers in standard form.

Solution :

Standard form:

Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.

(i) $6020000000000000=6.02 \times 1000000000000000$

$=6.02 \times 10^{15}$

$6020000000000000$ in standard form is $6.02 \times 10^{15}$.

(ii) $0.00000000000942=9.42 \times \frac{1}{1000000000000}$

$=9.42 \times \frac{1}{10^{12}}$

$=9.42 \times 10^{-12}$

$0.00000000000942$ in standard form is $9.42 \times 10^{-12}$. 

(iii) $0.00000000085=8.5 \times \frac{1}{10000000000}$

$=8.5 \times \frac{1}{10^{10}}$

$=8.5 \times 10^{-10}$

$0.00000000085$ in standard form is $8.5 \times 10^{-10}$.  

(iv) $846 \times 10^{7}=8.46 \times 100 \times 10^{7}$

$=8.46 \times 10^{2} \times 10^{7}$

$=8.46 \times 10^{9}$

$846 \times 10^7$ in standard form is $8.46 \times 10^{9}$.   

(v) $3759 \times 10^{-4}=3.759 \times 1000 \times 10^{-4}$

$=3.759 \times 10^{3} \times 10^{-4}$

$=3.759 \times 10^{-1}$

$3759 \times 10^{-4}$ in standard form is $3.759 \times 10^{-1}$.    

(vi) $0.00072984=\frac{7.2984}{10000}$

$=\frac{7.2984}{10^{4}}$

$=7.2984 \times 10^{-4}$

$0.00072984$ in standard form is $7.2984 \times 10^{-4}$. 

(vii) $0.000437 \times 10^{4}=\frac{4.37 \times 10^{4}}{10000}$

$=\frac{4.37 \times 10^{4}}{10^{4}}$

$=4.37 \times 10^{4} \times 10^{-4}$

$=4.37 \times 10^{0}$

$=4.37 \times 1$

$=4.37$

$0.000437 \times 10^4$ in standard form is $4.37$.   

(viii) $4 \div 100000 =\frac{4}{100000}$

$=\frac{4}{10^{5}}$

$=4 \times 10^{-5}$

$4 \div 100000$ in standard form is $4 \times 10^{-5}$.   

Tutorialspoint

Updated on: 10-Oct-2022

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