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Predicting the ones digit, copy and complete this table and answer the questions that follow.
Predicting the ones digit, copy and complete this table and answer the questions that follow. (a) Describe patterns you see in the ones digits of the powers, (b) Predict the ones digit in the following: 1. 4¹² 2. 9²⁰ 3. 3¹⁷ 4. 5¹⁰⁰ 5. 10⁵⁰⁰, (c) Predict the ones digit in the following: 1. 31¹⁰ 2. 12¹⁰ 3. 17²¹ 4. 29¹⁰
(a) Describe patterns you see in the ones digits of the powers.
(b) Predict the ones digit in the following: 1. 4¹² 2. 9²⁰ 3. 3¹⁷ 4. 5¹⁰⁰ 5. 10⁵⁰⁰
(c) Predict the ones digit in the following: 1. 31¹⁰ 2. 12¹⁰ 3. 17²¹ 4. 29¹⁰

Solution:

(a) We have to determine the pattern in the ones digits of the powers

x 1ˣ 2ˣ 3ˣ 4ˣ 5ˣ 6ˣ 7ˣ 8ˣ 9ˣ 10ˣ
1 1 2 3 4 5 6 7 8 9 10
2 1 4 9 16 25 36 49 64 81 100
3 1 8 27 64 125 216 343 512 729 1000
4 1 16 81 256 625 1296 2401 4096 6561 10000
5 1 32 243 1024 3125 7776 16807 32768 59049 100000
6 1 64 729 4096 15625 46656 117649 262144 531441 1000000
7 1 128 2187 16384 78125 279936 823543 2097152 4782969 10000000
8 1 256 6561 655356 390625 1679616 5764801 16777216 43046721 100000000
Ones digits of the power 1 2, 4, 8, 6 3, 9, 7, 1 4, 6 5 6 7, 9, 3, 1 8, 4, 2, 6 9, 1 0

 (b) We have to find the ones digit in the following.

1. Ones digit in 4¹² is 6

2. Ones digit in 9²⁰ is 1

3. Ones digit in 3¹⁷ is 3

4. Ones digit in 5¹⁰⁰ is 5

5. Ones digit in 10⁵⁰⁰ is 0

(c) We have to find the ones digit in the following.

1. Ones digit in 31¹⁰ is 1

2. Ones digit in 12¹⁰ is 4

3. Ones digit in 17²¹ is 7

4. Ones digit in 29¹⁰ is 1

✦ Try This: Express 14 billion litres of liquid in standard form.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

NCERT Exemplar Class 8 Maths Chapter 8 Problem 128

Predicting the ones digit, copy and complete this table and answer the questions that follow. (a) Describe patterns you see in the ones digits of the powers, (b) Predict the ones digit in the following: 1. 4¹² 2. 9²⁰ 3. 3¹⁷ 4. 5¹⁰⁰ 5. 10⁵⁰⁰, (c) Predict the ones digit in the following: 1. 31¹⁰ 2. 12¹⁰ 3. 17²¹ 4. 29¹⁰

Summary:

(a) The patterns in the ones digits of the powers is given above, (b) Ones digit in the following: 1. 4¹² is 6 2. 9²⁰ is 1 3. 3¹⁷ is 3 4. 5¹⁰⁰ is 5 5. 10⁵⁰⁰ is 0, (c) Ones digit in the following: 1. 31¹⁰ is 1 2. 12¹⁰ is 4 3. 17²¹ is 7 4. 29¹⁰ is 1

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