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

The table shows the average distance from each planet in our solar system to the sun.

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	$108, 200, 000$

Order the planets from closest to the sun to farthest from the sun.

Accepted Answer

We have given the distances of the planets of our solar system to the Sun. We have to arrange these distances from closest to the Sun to farthest from the Sun.

We have written the distances in standard form as shown below-

Celestial body Distance (km) Distance (km) Standard notation

Earth $149, 600, 000$ $1.496 \times 10^{8}$

Jupiter $778, 300, 000$ $7.783 \times 10^{8}$

Mars $227, 900, 000$ $2.279 \times 10^{8}$

Mercury $57, 900, 000$ $5.97 \times 10^{7}$

Neptune $4, 497, 000, 000$ $4.497 \times 10^{8}$

Pluto $5, 900, 000, 000$ $5.9 \times 10^{9}$

Saturn $1, 427, 000, 000$ $1.427 \times 10^{9}$

Uranus $2, 870, 000, 000$ $2.87 \times 10^{9}$

Venus $108, 200, 000$ $1.082 \times 10^{8}$

We know that the number with the higher power of $10$ or the larger exponent is the larger number, and if the powers are the same, then compare the numbers that precede the multiplication sign.

We can see that the distance of the Sun from the Mercury has the lowest power of $10$ . i.e. $10^{7}$ . So, this distance is the shortest. i.e. Mercury is closest to the Sun.

The distance of the Earth, Jupiter, Mars, Neptune and Venus have the same power of $10$ . Similarly, Pluto, Saturn and Uranus have the same power of $10$ . So, for these we compare the numbers that precede the multiplication sign.

The decimals can be compared by comparing the whole part or if the whole part is the same then, we can compare their tenth, hundredths, or thousandth places.

We can see $1.082 < 1.496 < 2.279 < 4.497 < 7.783$ , and $1.427 < 2.87 < 5.9$ .

Now, we can write these distances in ascending order-

$5.97 \times 10^{7} < 1.082 \times 10^{8} < 1.496 \times 10^{8} < 2.279 \times 10^{8} < 4.497 \times 10^{8} < 7.783 \times 10^{8} < 1.427 \times 10^{9} < 2.87 \times 10^{9} < 5.9 \times 10^{9}$

Thus, the order of the planets from closest to the Sun to farthest from the Sun-

$Mercury < Venus < Earth < Mars < Jupiter < Saturn < Uranus < Neptune < Pluto$ .

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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