Problem 51 - Prealgebra

Question

Divide and round answers to the nearest hundredth. $$5,679 \div 30.9$$

Step-by-Step Solution

Answer

The result is approximately 183.77.

Step 1: Convert Division into Decimal

First, let's perform the division of the numbers provided: 5,679 divided by 30.9. Use a calculator to divide these two numbers to get a decimal result.

Step 2: Calculate the Division

Using a calculator, divide 5,679 by 30.9. The result will be approximately 183.7741.

Step 3: Round the Answer

Now, round the result obtained, 183.7741, to the nearest hundredth. The hundredth place is the second digit after the decimal point. In this case, the digit in the hundredth place is 7, and the digit after it is 4. Since 4 is less than 5, we round down: 183.77.

Key Concepts

Understanding Decimal Division

Decimal division involves dividing numbers where one or both numbers have digits after the decimal point. It’s similar to regular division, but you must be cautious about placing the decimal in the right spot in the quotient. Start by converting the division into decimal form. Here, you divide two numbers and get a result with decimal points. For example, to divide 5,679 by 30.9, you can use a calculator. This helps in accurately positioning the decimal point in your answer. Be sure your answer reflects the real value,

• Avoid misplacing the decimal point.
• Ensure precision for correct results.

Decimal division is straightforward once you grasp how to manage the decimal places! Keep practicing with a calculator and soon you will master it.

Steps for Rounding Numbers

Rounding numbers trims off extra digits while keeping the number close to its original value. This makes it more manageable without being exactly accurate. The concept of rounding affects everyday decisions and estimations. Here's how you do it:

• Identify which place you are rounding to, like the nearest tenth or hundredth.
• Look at the digit immediately to the right of your target place.
• If this digit is 5 or greater, round up the target digit by one.
• If it's less than 5, keep the target digit as it is.

By focusing on these steps, rounding becomes a simple task. Once you get the hang of it, you’ll find it incredibly useful for simplifying calculations.

Rounding to the Nearest Hundredth

Rounding to the nearest hundredth means focusing on the second digit after the decimal point. This is particularly useful in many applications like financial calculations where precision is crucial. To achieve this, follow these steps:

• Determine the second digit after the decimal point. This is the hundredth place.
• Consider the third digit after the decimal point (the thousandth place) as the decider for rounding.
• If this decider digit is 5 or more, increase the hundredth place by 1.
• If the decider is less than 5, leave the hundredth place unchanged.

An example from before: 183.7741 rounded to the nearest hundredth becomes 183.77, as 4 (the decider) is less than 5. This simple process makes handling decimals precise and consistent.