1.

Consider the expression.

6.90105=(0.100+)2

You can solve for using a technique called successive approximations.

Step 1: If you assume that is very small compared to 0.100, such that 0.100+0.100, then your first approximation of (call it 1) can be calculated as

6.90105=1(0.100)2

Calculate the first approximation of . Express all answers to three or more significant figures.

1=

Step 2: Now, take your first approximation of and plug it into the full equation.

6.90105=2(0.100+1)2

Calculate the second approximation of .

Step 3: Each successive approximation uses the value from the previous approximation.

6.90105=3(0.100+2)2

Calculate the third approximation of .

3=

Step 4: Continue this process until two x values agree within the desired level of precision. Calculate the fourth and fifth approximations of .

4=

x5=

which values are the first to agree to two significant figures?

1 and 2, 3 and 4, 4 and 5, x2 and 3

Which values are the first to agree to three significant figures?

1 and 2, 4 and 5, 2 and 3, 3 and 4