Answer:
0.98994949366117
√0.98 = 0.98994949366117
Step 1:
Divide the number (0.98) by 2 to get the first guess for the square root.
First guess = 0.98/2 = 0.49.
Step 2:
Divide 0.98 by the previous result. d = 0.98/0.49 = 2.
Average this value (d) with that of step 1: (2 + 0.49)/2 = 1.245 (new guess).
Error = new guess - previous value = 0.49 - 1.245 = 0.755.
0.755 > 0.01. As error > accuracy, we repeat this step again.
Step 3:
Divide 0.98 by the previous result. d = 0.98/1.245 = 0.7871485944.
Average this value (d) with that of step 2: (0.7871485944 + 1.245)/2 = 1.0160742972 (new guess).
Error = new guess - previous value = 1.245 - 1.0160742972 = 0.2289257028.
0.2289257028 > 0.01. As error > accuracy, we repeat this step again.
Step 4:
Divide 0.98 by the previous result. d = 0.98/1.0160742972 = 0.9644963982.
Average this value (d) with that of step 3: (0.9644963982 + 1.0160742972)/2 = 0.9902853477 (new guess).
Error = new guess - previous value = 1.0160742972 - 0.9902853477 = 0.0257889495.
0.0257889495 > 0.01. As error > accuracy, we repeat this step again.
Step 5:
Divide 0.98 by the previous result. d = 0.98/0.9902853477 = 0.9896137535.
Average this value (d) with that of step 4: (0.9896137535 + 0.9902853477)/2 = 0.9899495506 (new guess).
Error = new guess - previous value = 0.9902853477 - 0.9899495506 = 0.0003357971.
0.0003357971 <= 0.01. As error <= accuracy, we stop the iterations and use 0.9899495506 as the square root.
So, we can say that the square root of 0.98 is 0.989 with an error smaller than 0.01 (in fact the error is 0.0003357971). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(0.98)' is 0.9899494936611666.
Note: There are other ways to calculate square roots. This is only one of them.
To round it to the tenths, it's 1
To round to the hundredths, it's.99
Thousandth is.990
