Question

Mass of the earth is (5.97×10²⁴) kg and mass of the Jupiter is (1.90×10²⁷) kg. what is the total mass of the two ?

Chapter- exponents and power

Answer 1

Mass of Jupiter=1.9×1027㎏=M1

Mass of Sun=1.99×1030㎏=M2

Mean distance of Jupiter from Sun=7.8×1011m=r

G=6.67×10−11N㎡㎏−2

Gravitational Force, F=r2GM1M2

F=(7.8×1011)26.67×10−11×1.9×1027×1.99×1030

F=4.16×1023N

Answer 2

${\large{\bold{\sf{\underline{LETS \: UNDERSTAND \: THE \: QUESTION\; FIRST :- }}}}}$

this is a question the exponents and power in which it is given that the mass of the earth is (5.97×10²⁴) kg and mass of the Jupiter is (1.90×10²⁷) kg and we need to do the total of these two masses .

Let's solve it !!

$\rule{150}{2}$

${\large{\bold{\sf{\underline{SOLUTION:-}}}}}$

( 1905.97 × 10²⁴ ) kg

$\rule{150}{2}$

${\large{\bold{\sf{\underline{FULL \; SOLUTION :-}}}}}$

${\bold{\sf{:\implies total \: mass \: = \: (5.97 \times 10^{24} + 1.90 \times {10}^{27})kg}}}$

${\bold{\sf{:\implies total \: mass \: = \: (5.97 \times 10^{24} + 1.9 \times {10}^{24} \times {10}^{3} )kg}}}$

${\bold{\sf{:\implies total \: mass \: = \: (5.97 + 1.9 \times {10}^{3} ) {10}^{24} \: kg}}}$

${\bold{\sf{:\implies total \: mass \: = \: (5.97 + 1900) {10}^{24} \: kg}}}$

${\bold{\sf{:\implies total \: mass \: = \: (1905.97 \times {10}^{24} )\: kg}}}$

$\rule{150}{2}$

${\large{\bold{\sf{\underline{KNOW \; MORE :-}}}}}$

To express large numbers in standard form

recall that any number can be expressed in a standard form as a decimal number between 1.0 and 10 , including 1.0 multiplyed by a power of 10 .

Thus , 657293 = 6.57293 × 10⁵ is the standard form of 657293 .

To express small numbers in standard form

very small numbers too can be expressed in standard form just like a very large numbers by writing the number in a form a × 10^n , where is a decimal number such that 1 ≤ a < 10 and n is an integer (negative for very small numbers and positive for very large numbers)