(4) Write any three rational numbers between the two numbers given below.
(i) 0.3 and -0.5 (ii) -2.3 and -2.33
(iii) 5.2 and 5.3 (iv)-4.5 and -4.6
Answers
Answer:
(i) 0.2, 0.1, -0.1
(ii) -2.31, -2.32, -2.322
(iii) 5.21, 5.22, 5.33
(iv) -4.51, -4.52, -4.53
Step-by-step explanation:
Answer:
Step-by-step explanation:
Example between 2 and 2.5?
2 + 2.5 = 4.5
4.5 ÷ 2 = 2.25
2.25 is a rational number between 2 and 2.5
but there are infinitely many more such numbers.
Example between 1¼ and 1½
1¼ + 1½ = 2 34
2 34÷2=138
138 is a rational number between 1¼ and 1½
but there are infinitely many more such numbers, for example:
→ the average of your first number and the average
→ the average of your second number and the previous average
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WEIGHTED AVERAGE METHOD:
The weighted average of rational numbers A and B
is a rational number between A and B:
You can use any integers for the weighted average. I’ll use double (2) and triple (3) with 2+3=5 for the divisor:
Double one number
Triple the other number
Add double-A plus triple-B
Divide by five (2+3=5)
Example between 4 and 4.5?
2 × 4 = 8
3 × 4.5 = 13.5
8 + 13.5 = 21.5
21.5 ÷ 5 = 4.3
(which happens to be 35 of the way from 4 to 4.5)
Example between 1¼ and 1½
2 × 1¼ = 2½
3 × 1½ = 4½
2½ + 4½ = 7
7 ÷ 5 = 125
(which happens to be 35 of the way from 1¼ to 1½)
Remember … you can use any multiples as long as you divide by the sum of the multiplicands.
Multiply A × 57
Multiply B × 43
Sum those products, then divide by 100 (57+43=100)
HOW TO USE A PROGRAMMABLE CALCULATOR
to find random rational numbers between _ and _
(between A and B, any rational or irrational values, A < B
This method is demonstrated with the
Example: Between 3 and 3.5 (directly entering each number as needed)
Example: Between e and π
(using variables A and B, which converts e and π to rational numbers in memory)
Example: Between 0.00001 and 0.000011
(using variables, which lets me re-use my prior typing)
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