Problem 83 - Prealgebra

Question

Compute the quotient \(5 / 94\), and round your answer to the nearest hundredth.

Step-by-Step Solution

Answer

The quotient of 5 divided by 94, rounded to the nearest hundredth, is 0.05.

Step 1: Perform the Division

To divide 5 by 94, you can either perform long division manually or input it into a calculator. Performing this division gives 5 divided by 94 equals approximately 0.0531914893617.

Step 2: Round to Nearest Hundredth

After obtaining the quotient 0.0531914893617 from the division, identify the hundredth position, which is the second digit after the decimal point (5 in this case). Since the third digit after the decimal is 3, which is less than 5, you round the hundredth position down and thus, round 0.0531914893617 to 0.05.

Key Concepts

Rounding

Rounding is a useful mathematical technique that simplifies numbers, making them easier to work with. When you round a number, you adjust it to a nearby value that is less precise. This helps in reducing complexity without losing the essential information of the number.

For instance, in the context of division, rounding usually involves adjusting the result to a certain decimal place to make it more manageable. When you have a long decimal like 0.0531914893617, rounding it to a shorter version simplifies the number.

Generally, rounding follows these rules:

• If the digit after the rounding place is 5 or more, increase the last retained digit by one.
• If the digit is less than 5, keep the last retained digit the same.

This way, rounding helps in maintaining accuracy while simplifying the complexity of decimal numbers.

Quotient

The quotient is the result you get when you divide one number by another. It represents how many times the divisor can fit into the dividend. In our example, dividing 5 by 94, the quotient is the result of this division.

When discussing the quotient:

• The dividend is the number being divided, which is 5 in this case.
• The divisor is the number you are dividing by, which is 94.
• The quotient is approximately 0.0531914893617 after you divide 5 by 94.

Understanding the quotient gives you insight into how one number can be broken into parts by another. It's essential in many mathematical calculations and real-world problem solving.

Hundredth Place Rounding

Rounding to the hundredth place involves focusing on the second place after the decimal point. The hundredth place helps in obtaining a number that is precise enough for general use, but not overly detailed.

When rounding to the hundredth:

• Identify the hundredth place by locating the second digit after the decimal point.
• Check the digit immediately after, which is the thousandth place, to see if rounding is needed.
• If the thousandth place digit is 5 or more, round up the hundredth place by one.
• If it is less than 5, keep the hundredth place digit unchanged.

In the exercise, 0.0531914893617 is rounded to 0.05 because the thousandth place digit is 3, which is less than 5. This precise rounding ensures accuracy while keeping numbers manageable.