Page 273 - Math_Genius_V1.0_C8_Flipbook

E:\Working\Focus_Learning\Math_Genius-8\Open_Files\15_Chapter_11\Chapter_11
\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

Comparing Very Large and Very Small Numbers

In 2024, the estimated total population of India was approximately 1.45 billion.
Suppose, we want to compare the population of India, with the population of the world, which
was approximately 8.16 billion; then

Population of India = 1.45 billion = 1.45 × 10 9
Population of world = 8.16 billion = 8.16 × 10 9 Knowledge Desk
.
Population of India 14510 9 1 Googol is an official name for a
×
Therefore, = = ((approx.) large number 10 100 or ten to the
.
×
Population of World 81610 9 6 power of one hundred. In decimal
So, the population of India is about 1 part of the total notation, it is written as the digit 1
population of the world. 6 followed by one hundred zeros.
Before comparing very large or small numbers, we first
convert them to their standard exponential form and then divide them.
• If two numbers in standard form have the same power of 10, then the number with the larger
24
24
factor is greater. For example, 8.72 × 10 < 9.4326 × 10 .
• If two numbers in standard form have the same factor, then the number with the larger power
8
4
of 10 will be greater. For example, 8.72 × 10 > 8.72 × 10 .
• If two numbers in standard form have the different factors and the different power of 10, then
the number with the higher power of ten (i.e, the larger exponent) is the larger number.
For example, 8.72 × 10 > 9.4326 × 10 .
24
23
Example 10: Investigating Solar System: The table shows the average distance from each planet
in our solar system to the sun.

Planet Distance from Sun (km) Scientific Notation

Earth 149,600,000 1.496 × 10 8
Jupiter 778,300,000
Mars 227,900,000

Mercury 57,900,000
Neptune 4,497,000,000
Saturn 1,427,000,000

Uranus 2,870,000,000
Venus 108,200,000

(a) Complete the table by expressing the distance from each planet to the Sun in
scientific notation.

(b) Order the planets from closest to the sun to farthest from the sun.
Solution: (a) Scientific notation of distance from Sun to

Earth = 149600000 km = 1.496 × 10 km
8
8
Jupiter = 778300000 km = 7.783 × 10 km
Mars = 227900000 km = 2.279 × 10 km
8
271 Exponents and Powers