Question

b. calculate the sum vertically.

0.137
+ 0.284
-------
.

Explanation:

Step1: Add thousandths place

Add the digits in the thousandths place: \(7 + 4 = 11\). Write down \(1\) and carry over \(1\) to the hundredths place.

Step2: Add hundredths place

Add the digits in the hundredths place with the carried over \(1\): \(3 + 8 + 1 = 12\). Write down \(2\) and carry over \(1\) to the tenths place.

Step3: Add tenths place

Add the digits in the tenths place with the carried over \(1\): \(1 + 2 + 1 = 4\). Write down \(4\) in the tenths place.

Step4: Add ones place

The ones place for both numbers is \(0\), so \(0 + 0 = 0\) in the ones place.

Putting it all together, the sum is \(0.421\).

Answer:

\(0.421\) (The boxed answer would be \(\boxed{0.421}\) if we follow the LaTeX boxed format for the final answer, but as per the initial instruction, we can present it as is here.)