Page 92 - Start Up Mathematics_7

8
Solution: (a) 384,000,000 m = 3.84 × 100,000,000 m = 3.84 × 10 m
9
(b) 1,400,000,000 m = 1.4 × 1,000,000,000 = 1.4 × 10 m
11
(c) 100,000,000,000 = 1 × 100,000,000,000 = 1 × 10 stars
10
(d) 12,000,000,000 years = 1.2 × 10,000,000,000 = 1.2 × 10 years
(e) 300,000,000,000,000,000,000 m = 3 × 100,000,000,000,000,000,000
20
= 3 × 10 m
(f) 1,027,000,000 = 1.027 × 1,000,000,000 = 1.027 × 10 9
Example 19: Compare the following numbers:
5
12
8
(a) 1.7 × 10 ; 8.5 × 10 (b) 9.8 × 10 ; 1.3 × 10 6
Solution: (a) These numbers are in standard form. Therefore, we just need to compare the powers
12
8
of 10. The power of 10 is greater in 1.7 × 10 in comparison to 8.5 × 10 .
8
12
∴ 1.7 × 10 > 8.5 × 10 .
(b) Since the numbers are in standard form, the number having greater power of 10
5
6
is greater. ∴ 9.8 × 10 < 1.3 × 10 .
17
Example 20: The mass of a particle is 3.84 × 10 grams. Find the mass of a particle 5,000 times
bigger than it.
17
Solution: Mass of a particle = 3.84 × 10 grams
17
Mass of a particle 5,000 times bigger = 3.84 × 10 × 5,000 grams
3
17
21
= (3.84 × 10 ) × (5 × 10 ) = 19.2 × 10 17 + 3 = 1.92 × 10 grams
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.
8
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 1,240 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.

At a Glance

1. If p is a non-zero rational number and n a natural number, then p × p × p × ... n times is equal
n
to p and is read as ‘p raised to the power n’.

84