Page 77 - ICSE Math 7

EXERCISE 5.3

1. Write the following numbers in expanded form.
(a) 3,56,780 (b) 46,00,349 (c) 35,79,124
2. Write the following in scientific notation or standard form.

(a) 220,000,000,000 (b) 4,89,21,34,76,000 (c) 0.00000006532
3. How many seconds are there in a leap year? Express it in standard form.
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4. If the velocity of light is 3.0 × 10 metres per second, calculate the distance travelled by light in
a light year and express it in standard form.
[Hint: One light year = Distance travelled by light in a year.]
5. The speed of an airplane is 885 km per hour. Find the distance covered by the airplane in
3 hours and 20 minutes. Also, express the distance in scientific notation.
6. Write the following in standard form.
(a) The mass of Uranus is 86,800,000,000,000,000,000,000,000 kg.
(b) The distance between Saturn and Uranus is 1,439,000,000,000 m.

Application of Laws of Exponents
In this section, we will learn various real life uses of exponents. Exponents are used regularly in
measuring area and volume. For example, area of a square field having side 32 m is calculated as
2
2
32 m × 32 m = (32 m) = 1,024 m and the volume of a cube of side ‘a’ unit is given by (a × a × a)
3
cubic unit or a cubic unit.
Let’s take another example.
A certain bacterium splits into 2 bacteria every hour. There is 1 bacterium on a slide. Each bacterium on
the slide splits once per hour. We calculate the number of bacteria after 6 hours in the following way.
Each hour, the number of, bacteria is a power of 2.
1
After 1 hour: 1 × 2 = 2 or 2 bacteria on the slide.
2
After 2 hours: 2 × 2 = 4 or 2 bacteria on the slide. After 1 hour
3
After 3 hours: 4 × 2 = 8 or 2 bacteria on the slide. After 2 hours
6
After the 6th hours, there will be 2 bacteria. After 3 hours
6
2 = 2 × 2 × 2 × 2 × 2 × 2 = 64
So, after 6 hours, there will be 64 bacteria on the slide.
1
2
Example 20: The number of diagonals of an n-sided figure is (n – 3n). Use the formula to find the
number of diagonals for an 8-sided figure. 2
1
2
Solution: Given formula for the number of diagonals of an n-sided figure is (n – 3n).
2
\ Number of diagonals for an 8-sided figure.
1
2
= (8 – 3 × 8) (Substituting n = 8)
2
1
= (64 – 24)
2
1
= × 40 = 20
2
An 8-sided figure has 20 diagonals. The same can be verified by sketching the diagonals.

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