Adding Decimal Numbers Explained

The question asks us to find the sum of the following decimal numbers: 0.296, 2.96, 29.6, and 296.

To add decimal numbers correctly, it is important to align the decimal points vertically. We can add zeros to the right of the decimal point for numbers with fewer decimal places so that all numbers have the same number of decimal places. This helps in aligning the place values properly.

Let's write the numbers, aligning the decimal points:

  0.296
  2.960  (added a zero)
 29.600  (added two zeros)
296.000  (added three zeros; the decimal point is after the whole number 296)
-------

Now, we can add the numbers column by column, starting from the rightmost column:

• In the thousandths place (the third digit after the decimal point): \(6 + 0 + 0 + 0 = 6\).
• In the hundredths place (the second digit after the decimal point): \(9 + 6 + 0 + 0 = 15\). Write down 5 and carry over 1 to the tenths place.
• In the tenths place (the first digit after the decimal point): \(1\) (carry over) \(+ 2 + 9 + 6 + 0 = 18\). Write down 8 and carry over 1 to the units place (before the decimal point).
• Place the decimal point after the tenths place.
• In the units place: \(1\) (carry over) \(+ 0 + 2 + 9 + 6 = 18\). Write down 8 and carry over 1 to the tens place.
• In the tens place: \(1\) (carry over) \(+ 0 + 0 + 2 + 9 = 12\). Write down 2 and carry over 1 to the hundreds place.
• In the hundreds place: \(1\) (carry over) \(+ 0 + 0 + 0 + 2 = 3\). Write down 3.

So, the sum is 328.856.

Let's perform the addition formally:

   0.296
   2.960
  29.600
+ 296.000
---------
 328.856

Therefore, \(0.296 + 2.96 + 29.6 + 296 = 328.856\).

Comparing this result with the given options, we find that 328.856 matches one of the options.

The value that comes in place of ? is 328.856.

Revision Table: Key Concepts in Decimal Addition

Additional Information: Understanding Decimal Numbers

Decimal numbers are a way of representing fractions where the denominator is a power of ten. The digits to the right of the decimal point represent fractional parts.

• The first digit to the right of the decimal point is the tenths place (\(1/10\)).
• The second digit is the hundredths place (\(1/100\)).
• The third digit is the thousandths place (\(1/1000\)), and so on.

Adding decimal numbers is a fundamental arithmetic operation. It is widely used in various real-life situations involving measurements, money, and calculations where precision is required. Always remember to align the decimal points before adding.