Exponents And Powers Test

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Exponents And Powers Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

The population of England is 5.11 × 10⁷ and that of Northern Ireland is 1.82 × 10⁶. What is the difference between the populations, in standard form?

A
4.192 × 10⁶

B
4.928 × 10⁷

C
5.923 × 10⁷

D
6.723 × 10⁷

Solution

Population of England = 5,11,00,000
Population of Northern Ireland = 18,20,000
Difference = 5,11,00,000 - 18,20,000 = 4.928 × 10⁷
Question 2
1 / -0

The distance between Mercury and Mars is approximately 2,05,00,00,000 miles. How can this distance be represented in standard index form?

A
2.05 × 10⁹ miles

B
2.50 × 10⁸ miles

C
2.05 × 10⁸ miles

D
2.50 × 10⁷ miles

Solution

The distance from Mercury to Mars is 2,05,00,00,000 miles.
Standard index form: A × 10ⁿ

As it is a big number, n will be positive.
Hence, the answer is 2.05 × 10⁹ miles.
Question 3
1 / -0

The height of World Trade Centre is 4.696 × 10⁵ mm. What will be its height when written in usual form?

A
46,96,000 mm

B
4,69,600 mm

C
4,696 mm

D
4,69,60,000 mm

Solution

The height has been given in standard form. When written in usual form, we get
4.696 × 10⁵ mm = 4.696 × 1,00,000 = 4,69,600 mm
Question 4
1 / -0

The mass of the Sun is approximately 2 × 10³⁰ kg and the mass of the Earth is 6 × 10²⁴ kg. What is the sum of both the masses?

A
1.785573 × 10²⁶ kg

B
2.000006 × 10³⁰ kg

C
4.0000006 × 10³⁰ kg

D
8 × 10⁵⁴ kg

Solution

Mass of Sun = 2 × 10³⁰ kg
Mass of Earth = 6 × 10²⁴ kg

Sum of masses = 2 × 10³⁰ + 6 × 10²⁴

= (2000000 + 6)10²⁴
= 2.000006 × 10³⁰kg
Question 5
1 / -0

If 6^x + 6^{x - 1} = 42, then 2^{x - 1} equals

A
0

B
1

C
2

D
3

Solution

6^x + 6^{x - 1} = 42
Or 6^{x - 1}(6 + 1) = 42

After taking 6^{x - 1}common and simplifying, we get
6^{x - 1}= 6
Or x = 2

Now, 2^{x - 1} = 2¹ = 2

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Re-Attempt Weekly Quiz Competition

Exponents And Powers Test - 5

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Exponents And Powers Test - 5

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Question 1

4.192 × 106

4.928 × 107

5.923 × 107

6.723 × 107

Solution

Question 2

2.05 × 109 miles

2.50 × 108 miles

2.05 × 108 miles

2.50 × 107 miles

Solution

Question 3

46,96,000 mm

4,69,600 mm

4,696 mm

4,69,60,000 mm

Solution

Question 4

1.785573 × 1026 kg

2.000006 × 1030 kg

4.0000006 × 1030 kg

8 × 1054 kg

Solution

Question 5

0

1

2

3

Solution

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4.192 × 10⁶

4.928 × 10⁷

5.923 × 10⁷

6.723 × 10⁷

2.05 × 10⁹ miles

2.50 × 10⁸ miles

2.05 × 10⁸ miles

2.50 × 10⁷ miles

1.785573 × 10²⁶ kg

2.000006 × 10³⁰ kg

4.0000006 × 10³⁰ kg

8 × 10⁵⁴ kg