Would use the algorithm for solving square root.
For square root, √n
x₁ = 0.5(x₀ + n/x₀)
(This formula is known and for square root, and can be derived using Newton-Raphson's approximation equation)
Where x₀ is the initial guess. x₁ becomes the new guess.
For √100.6 let our initial guess be 10, x₀ = 10, n = 100.6
Our approximation shall be to 3 decimal places. Once we get the same answer twice we stop the algorithm.
x₀ = 10, x₁ = 0.5(x₀ + n/x₀), x₁ = 0.5(10 + 100.6/10) = 10.030, x₁ = 10.030
x₂ = 0.5(x₁ + n/x₁), x = 0.5(10.030 + 100.6/10.030) ≈10.015, x₂ ≈ 10.030 (to 3 decimal places)
Since x₂≈ x₁, the algorithm stops.
So the √100.6 is ≈ 10.030 to 3 decimal places.
I hope this helps.
Answer:
87,500
Step-by-step explanation:
Since the last 2 digits arent 5 or greater than 5 it can not be rounded to the next hundred.
Answer:
26 over 3 =2
------ = 8.667
3
Convert mixed number to improper fraction
5 and 3 over 45
3
4
= ( 5 × 4 ) over 4
5 × 4
4
+ 3 over 4
3
4
= ( 20 + 3 ) over 4
20 + 3
4
= 23 over 4
23
4
Step 1 of 2: Add, sub-step b: Convert mixed number to improper fraction.
Convert mixed number to improper fraction
2 and 11 over 122
11
12
= ( 2 × 12 ) over 12
2 × 12
12
+ 11 over 12
11
12
= ( 24 + 11 ) over 12
24 + 11
12
= 35 over 12
35
12
Step 1 of 2: Add, sub-step c: Find common denominator.
Find common denominator
23 over 4
23
4
+ 35 over 12
35
12
= ( 23 × 3 ) over ( 4 × 3 )
23 × 3
4 × 3
+ ( 35 × 1 ) over ( 12 × 1 )
35 × 1
12 × 1
= 69 over 12
69
12
+ 35 over 12
35
12
12 is the least common multiple of denominators 4 and 12. Use it to convert to equivalent fractions with this common denominator.
Step 1 of 2: Add, sub-step d: Add.
Add
69 over 12
69
12
+ 35 over 12
35
12
= ( 69 + 35 ) over 12
69 + 35
12
= 104 over 12
104
12
$3.15 because 5,25 divided by 5 is 1.05 times 3
