Today our topic of discussion is Real Numbers Exercises 1.
Real Numbers Exercises 1
Exercises 1
- Which numbers are irrational?
1) 0.3
2) ✓(16/9)
3) ✓(8/27, 3)
4) 5/(✓3))
- If a, b, c, d are four consecutive natural numbers which one of the following will be a whole squared?
1) abcd
2) ab + cd
3) abcd +1
4) abcd-1
- How many primes are there from 1 to 10?
1) 3
2) 4
3) 5
4) 6
- Which one is the set of all integers?
1) \ …, – 4 ,-2,0,2,4,…\
2) \ …, – 2 ,-1,0,1,2,…\
3) \ …, – 3 ,-1 0,1,3,…\
4) \{0, 12, 3, 4\}
- In case of real numbers
(i) Square of an odd integer is odd.
(ii) Product of two even numbers is even.
(iii) Square root of a number that is not whole squared is an irrational number.
Which one is true?
1) i and ii
2) i and iii
3) ii and iii
4) i, ii and iii
- Product of three consecutive numbers will always be divisible by which of the following numbers?
1) 5
2) 6
3) 7
4) 11
- If a and b are two consecutive even numbers, then which of the following numbers is odd?
1) a2
2) 62
3) a ^ 2 + 1
4) b ^ 2 + 2
- If a and b are two integers, then what should be added to a ^ 2 + b ^ 2 to obtain
a whole squared ?
1) -ab
2) ab
3) 2ab
4) ab
- Prove that the following numbers are irrational.
1) ✓5)
2) ✓(7)
3)✓10
10.1) Find two irrational numbers between 0.31 and 0.12.
2) Find a rational and an irrational number between 1/✓2 and ✓2
11.1) Prove that square of an odd integer is an odd integer.
2) Prove that product of any two consecutive even integers is divisible by 8.
- Convert the following into repating decimal fractions:
1) 1/6
2) 7/11
3 2/9 3)
4) 3 8/15
- Convert into simple fractions;
1) 0.2
2) 0.35
3) 0.13
4) 3.78
5) 6.2309
- Express the follwoing into similar repeating decimal fractions:
1) 2.23, 5.235
2) 7.26, 4.237
3) 5.7, 8.34, 6.245
4) 12.32, 2.19, 4.3256
- Add;
1) 0.4 dot 5 +0.1 dot 3 dot 4
2) 2.0 dot 5 +8.0 dot 4 + 7.018
3) 0 dot 6 +0. dot 9 dot 2 +0. dot 1 3 dot 4
- Subtract:
1) 3.4-2.13 3) 8.49 -5.
2) 5. dot 1 * 2 -3.4 dot 5
3) dot 5 dot 6
4) 19.34 dot 5 -13.2 dot 3 4 dot 9
- Multiply:
1) 0. dot 3 *0. dot 6
2) 2. dot 4 *0. dot 8i
3) 0.6 dot 2 *0. dot 3
4) 42. dot 1 dot 8 *0.2 dot 8
- Divide:
1) 0. dot 3 /0. dot 6
2) 0.3 dot 5 /1. dot 7
3) 2.3 dot 7 /0.4 dot 5
4) 1. dot 1 8 dot 5 /0. dot 2 dot 4
- Wrtite down values and approximate values up to 4 decimal places :
1) 12
2) 0.25
3) 1.34
4) 5.1302
- Write down which of the following numbers are rational and irrational:
1) 0.4
2) ✓9
3) ✓11
4) ✓6/3
5) ✓8/✓7
6) ✓27/✓48
7) (2/3)/(3/7)
8) 5.639
- Let n ^ 2 21. Let n = 2x – 1 , where x in N Prove that when divided by 8 gives 1 as remainder.
- ✓5 and 4 are two real numbers.
1) Specify which one is rational and which one is irrational.
2) Find two irrational numbers between ✓5 and 4.
3) Prove that sqrt(5) is an irrational number.
- Simplify:
1) (0. dot 3 *0.8 dot 3 )/(0.5*0. dot 1 )+0.3 dot 5 /0.0 dot 8
2) [(6.27 * 0.5) / \{(0.5 * 0.75) * 8.36\}] / \ (0.25 * 0.1) *(0.75*21. dot 3 )*0.5\
Read more: