Page 62 - Revised Maths Wisdom Class - 6

60 MATHS

Process completed, if 1 comes (obtained)
So, the series is 12, 6, 3, 10, 5, 16, 8, 4, 2, 1

(b) 15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1 (iii) 21, 64, 32, 16, 8, 4, 2, 1

Beside this, it is still only conjecture. Even today, many Mathematicians working on it, it remains an unsolved
problem as to whether Collatz’s conjecture is true!
Collatz’s conjecture is one of the most famous unsolved problems in maths.

Estimation

The estimation of a number is a reasonable guess of the actual value. Estimation means approximating a quantity
to the accuracy required. This is done by rounding off the numbers involved and getting a quick and rough answer.

ILLUSTRATIONS

Estimate 92 × 578
The first number, 92, can be rounded off to the nearest ten as 90.
The second number, 578, can be rounded off to the nearest hundred as 600.

Hence, the estimated product = 90 × 600 = 54,000.

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Exercise 4Bxercise 4B
1. What is the largest 6-digit number whose digit sum is 17?
2. What is the smallest 5-digit number whose digit sum is 8?
3. What is the largest 2-digit number whose digit sum is 16?

4. What is the smallest 3-digit number whose digit sum is 13?
5. What is the largest 4-digit number whose digit sum is 19?
6. Estimate the product (note: multiplicands should be round off according to their value)
(a) 8 × 86 = __________ (b) 126 × 978 = __________ (c) 1012 × 846 = __________

(d) 1876 × 7495 = __________ (e) 96 × 856 = __________ (f) 199 × 294 = __________

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REVIEW TIMEEVIEW TIME

COMPETENCY BASED QUESTIONS
A Oral Quiz Oral Quiz

1. How can you define palindromic number? 3. What is the magic number of ‘Kaprekar’.

2. What is the smallest number longer than 1000 4. How many digits are in Kaprekar constant?
that is palindromic? 5. What is the digit sum of 3-digit number ‘1 01’?

B Multiple-ChOiCe QuestiOns Multiple-ChOiCe QuestiOns
1. Largest 5 digit number whose digit sum is 14.
(a) 68000 (b) 98000 (c) 95000 (d) 90005