Problem 46 - Algebra A Combined Function

Question

Round each decimal to the given place value. $$ 68,936.543 \text { , nearest tenth } $$

Step-by-Step Solution

Answer

Rounding to the nearest tenth gives 68,936.5.

Step 1: Identify the place value

The place value we are asked to round to is the 'tenth'. In the number 68,936.543, the digit in the tenths place is the first digit to the right of the decimal point, which is 5.

Step 2: Look at the next digit

To determine how to round the digit in the tenths place, we need to look at the digit immediately to the right, which is the hundredths place. In this number, the digit in the hundredths place is 4.

Step 3: Apply rounding rules

According to rounding rules, if the digit in the next place (hundredths) is 5 or greater, we round up the tenths place. If it is less than 5, we leave the tenths place digit as it is. Here, the digit in the hundredths place is 4, which is less than 5. Therefore, we keep the 5 in the tenths place unchanged.

Step 4: Write the rounded number

Since the digit in the hundredths place is 4, we do not round up. So, the number rounded to the nearest tenth is 68,936.5.

Key Concepts

Tenth Place Value

When dealing with decimals, the place value system is similar to whole numbers but extends to the right of the decimal point as well. Each digit has its own specific place value. The 'tenth place' is the first position immediately right of the decimal point. For example, in the number 68,936.543, the digit '5' is in the tenth place.

This positioning is crucial because it determines the value the digit represents. In this case, '5' represents five-tenths or 0.5. Understanding where the tenth place is located in any decimal will help you determine which digit will be altered during the rounding process.

Rounding Rules

Rounding is a way to simplify numbers, and it follows specific rules depending on the digit right after the place you are rounding to. Let's focus on rounding to the nearest tenth:

• If the digit immediately next to the tenths place (hundredths place) is 5 or greater, you increase the tenths digit by 1.
• If that digit is less than 5, the tenths digit remains unchanged.

In our example, 68,936.543, the digit in the hundredths place is '4'. Since 4 is less than 5, the tenth place digit '5' remains unchanged according to these rounding rules. You simply need to focus on the hundredths digit to make a rounding decision.

Decimal Place Value

Understanding decimal place value helps in both identifying place values and performing rounding operations effectively. Each position to the right of the decimal point represents a fractional power of 10.

• The first place is the tenths (\(10^{-1}\))
• The second place is the hundredths (\(10^{-2}\))
• The third place is the thousandths (\(10^{-3}\))

In the decimal number 68,936.543, the digit '5' is in the tenths, '4' in the hundredths, and '3' in the thousandths place. Knowing this sequence and the importance of each position ensures you correctly identify and manipulate numbers when rounding.