Name: Use of Exponents to Express Small Numbers in Standard Form
Uploaded: 2019-07-19
Duration: 8 min 15 s
Description: In this video, we will learn how to express a number in its standard exponential form. Very large as well as very small numbers can be expressed in standard...

Question

Astronomy table shows the mass of the planets of the solar system.

Celestial body	Mass (kg)	Mass (kg) Standard notation
Sun	$1, 990, 000, 000, 000, 000, 000, 000, 000, 000, 000$	$1.99 \times 10^{30}$
Mercury	$330, 000, 000, 000, 000, 000, 000, 000$
Venus	$4, 870, 000, 000, 000, 000, 000, 000, 000$
Earth	$5, 970, 000, 000, 000, 000, 000, 000, 000$
Mars	$642, 000, 000, 000, 000, 000, 000, 000, 000, 000$
Jupiter	$1, 900, 000, 000, 000, 000, 000, 000, 000, 000$
Saturn	$568, 000, 000, 000, 000, 000, 000, 000, 000$
Uranus	$86, 800, 000, 000, 000, 000, 000, 000, 000$
Neptune	$102, 000, 000, 000, 000, 000, 000, 000, 000$
Pluto	$12, 700, 000, 000, 000, 000, 000, 000$
Moon	$73, 500, 000, 000, 000, 000, 000, 000$

Write the mass of each planet and the Moon in scientific notation.

Accepted Answer

We have given the masses of the planets of our solar system. We have to convert them into standard form.

We know that any number that we can write as the decimal number, between the numbers $1.0$ and $10.0$ , then multiplied by the power of the number $10$ , is known to be in the standard form.

For example-

The mass of the Sun $= 1, 990, 000, 000, 000, 000, 000, 000, 000, 000, 000 kg$ .

To convert this in standard form, we move the decimal point to the left side such that we get a decimal number between $1.0$ and $10.0$ . So, we move the decimal point $30$ places to the left side, and we get-

$1.99 \times 10^{30}$ .

Similarly, we can get the other numbers in standard forms as shown below-

Celestial body Mass (kg)
Mass (kg)

Standard notation

Sun $1, 990, 000, 000, 000, 000, 000, 000, 000, 000, 000$ $1.99 \times 10^{30}$

Mercury $330, 000, 000, 000, 000, 000, 000, 000$ $3.3 \times 10^{23}$

Venus $4, 870, 000, 000, 000, 000, 000, 000, 000$ $4.87 \times 10^{24}$

Earth $5, 970, 000, 000, 000, 000, 000, 000, 000$ $5.97 \times 10^{24}$

Mars $642, 000, 000, 000, 000, 000, 000, 000, 000, 000$ $6.42 \times 10^{29}$

Jupiter $1, 900, 000, 000, 000, 000, 000, 000, 000, 000$ $1.9 \times 10^{27}$

Saturn $568, 000, 000, 000, 000, 000, 000, 000, 000$ $5.68 \times 10^{26}$

Uranus $86, 800, 000, 000, 000, 000, 000, 000, 000$ $8.68 \times 10^{25}$

Neptune $102, 000, 000, 000, 000, 000, 000, 000, 000$ $1.02 \times 10^{26}$

Pluto $12, 700, 000, 000, 000, 000, 000, 000$ $1.27 \times 10^{22}$

Moon $73, 500, 000, 000, 000, 000, 000, 000$ $7.95 \times 10^{22}$

Celestial body	Distance (km)	Distance (km) Standard notation
Earth	$149, 600, 000$	$1.496 \times 10^{8}$
Jupiter	$778, 300, 000$
Mars	$227, 900, 000$
Mercury	$57, 900, 000$
Neptune	$4, 497, 000, 000$
Pluto	$5, 900, 000, 000$
Saturn	$1, 427, 000, 000$
Uranus	$2, 870, 000, 000$
Venus	$108, 200, 000$

Celestial body	Distance (km)	Distance (km) Standard notation
Earth	$149, 600, 000$	$1.496 \times 10^{8}$
Jupiter	$778, 300, 000$
Mars	$227, 900, 000$
Mercury	$57, 900, 000$
Neptune	$4, 497, 000, 000$
Pluto	$5, 900, 000, 000$
Saturn	$1, 427, 000, 000$
Uranus	$2, 870, 000, 000$
Venus	$108, 200, 000$

Element	Mass of atom (kg)
Titanium	$7.95 \times 10^{- 26}$
Lead	$3.44 \times 10^{- 25}$
Silver	$1.79 \times 10^{- 25}$
Lithium	$1.15 \times 10^{- 26}$
Hydrogen	$1.674 \times 10^{- 27}$

Element	Mass of atom (kg)
Titanium	$7.95 \times 10^{- 26}$
Lead	$3.44 \times 10^{- 25}$
Silver	$1.79 \times 10^{- 25}$
Lithium	$1.15 \times 10^{- 26}$
Hydrogen	$1.674 \times 10^{- 27}$

Element	Mass of atom (kg)
Titanium	$7.95 \times 10^{- 26}$
Lead	$3.44 \times 10^{- 25}$
Silver	$1.79 \times 10^{- 25}$
Lithium	$1.15 \times 10^{- 26}$
Hydrogen	$1.674 \times 10^{- 27}$

Important Questions on Exponents and Powers

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