Problem 49 - Prealgebra

Question

Problems Work each of the following problems on your calculator. If rounding is necessary, round to the nearest hundred thousandth. $$0.0503 \div 0.0709$$

Step-by-Step Solution

Answer

The result of \(0.0503 \div 0.0709\) is approximately 0.70943.

Step 1: Identify the Problem

We need to divide 0.0503 by 0.0709 and round the result to the nearest hundred thousandth.

Step 2: Setup the Calculation

Enter the division operation into your calculator as follows: \(0.0503 \div 0.0709\). This sets up the problem for calculation.

Step 3: Perform the Division

Press the equals button on your calculator to perform the division. The calculator will display the result.

Step 4: Round the Result

Take the result from your calculator and round it to the nearest hundred thousandth. The number displayed should help you decide the rounding based on the sixth decimal place.

Key Concepts

Division

Division is one of the four fundamental operations of arithmetic. It involves splitting a number into equal parts or groups. In the exercise above, we utilize division to determine how many times one number fits into another. This is represented by the division of 0.0503 by 0.0709.

To divide two decimal numbers, you follow these simple steps:

• Align the numbers according to their decimal points.
• Divide the two numbers as if they were whole numbers.
• Once done, place the decimal point in the quotient directly above where it is in the dividend.

This operation is straightforward when using a calculator as it performs the calculations instantly. It's important to remember that decimals make division unique, but the process remains manageable with practice and proper setup.

Calculator Usage

Using a calculator can simplify complex calculations, especially with decimal numbers. In the task, you're asked to use a calculator for dividing decimals to enhance accuracy and speed. Here's how you can effectively use a calculator for division:

• First, clear any previous entries by pressing the "clear" button.
• Enter the first number (the dividend), in this case, 0.0503.
• Press the division symbol (/).
• Enter the second number (the divisor), 0.0709.
• Press the equals (=) button to compute the result.

Modern calculators handle large decimal numbers without difficulty and will show you the answer almost instantly. This step ensures precision in your calculation, avoiding any manual errors.

Rounding Decimals

Rounding decimals is essential when a precise figure isn't necessary or when working within specified limits, like rounding to the nearest hundred thousandth as in the exercise. To round a decimal:

• Identify the decimal place to which you need to round. Here, it's the fifth decimal place, or the hundred thousandth.
• Look at the digit immediately following it in the sixth decimal place.
• If this trailing number is 5 or greater, round the number in the specified decimal place up by one. If it’s less than 5, keep the number as is.

For example, if your calculation resulted in a number such as 0.7090912, you would check the sixth digit, which is 1. This number is less than 5, so you would round down, resulting in 0.70909.

Rounding helps in simplifying results and making them more readable, especially in assignments where precision beyond a certain point isn’t necessary.