Problem 56 - Prealgebra

Question

Add or subtract as indicated. $$5+0.03+1.9$$

Step-by-Step Solution

Answer

The sum is 6.93.

Step 1: Understanding the Problem

We need to find the sum of three numbers: 5, 0.03, and 1.9. This involves straightforward addition of these decimals and a whole number.

Step 2: Align and Add

Align the decimal points: \[\begin{array}{c} 5.00 \+0.03 \+1.90 \\hline\end{array}\]Then, add the numbers column by column, starting from the rightmost column to the left.

Step 3: Column Addition

Starting from the rightmost column (hundredths): 0 + 3 + 0 = 3. Write 3 in the hundredths place. In the tenths column: 0 + 0 + 9 = 9. Write 9 in the tenths place. Finally, in the units column: 5 + 0 + 1 = 6. Write 6 in the units place.

Step 4: Write the Final Sum

Compile the results from each column of sums: \[ 6.93 \]Therefore, the sum of 5, 0.03, and 1.9 is 6.93.

Key Concepts

Decimal Alignment

When you're working with decimals, especially during addition, alignment of the decimal points is crucial. Imagine the chaos if your decimals weren't lined up correctly - it would lead to inaccurate results. To ensure precision:

• Align the numbers vertically in a way that each decimal point is directly underneath the others.
• It's okay to add extra zeros to the numbers to make the alignment clear, like turning 5 into 5.00.
• Every digit should have its own column, whether it's representing units, tenths, hundredths, and so on.

This practice of aligning decimal points makes the next step of addition much easier and prevents any accidental mix-ups between different place values.

Column Addition

Once your decimals are neatly aligned, it's time for the actual addition. Column addition is a step-by-step process:

• Begin with the rightmost column, which in decimals, is the smallest place value, like the hundredths.
• Work your way left, adding one column at a time. If the sum of a column exceeds 9, carry over the extra value to the next column on the left.
• This method is similar to regular addition but requires careful observation on where to carry over if needed.

By tackling one column at a time, you ensure each place value is correctly addressed, resulting in an accurate total.

Sum Calculation

After successfully adding each column, the final step involves summing them up. The results from each column you've calculated are then compiled into a single number.

• The digits from each column form the new decimal number.
• Make sure the decimal point in your answer aligns with the ones in your initial numbers, maintaining alignment right through to the answer.
• For example, from the numbers 5, 0.03, and 1.9, we end up with 6.93 after ensuring each column adds up correctly.

Applying careful sum calculation guarantees that your final answer is both precise and reliable.