Problem 45 - Prealgebra

Question

Problems Work each of the following problems on your calculator. If rounding is necessary, round to the nearest hundred thousandth. $$7 \div 9$$

Step-by-Step Solution

Answer

Rounded to the nearest hundred thousandth, 7 ÷ 9 is 0.77778.

Step 1: Understand the Division Problem

The problem given is to divide the number 7 by the number 9. This requires finding out how many times 9 fits into 7.

Step 2: Perform the Division

Using a calculator, divide 7 by 9. Enter 7 as the dividend and 9 as the divisor to execute the calculation. This will give you the exact decimal result of the division.

Step 3: Read the Calculator Output

After performing the division, the calculator will display the result as a decimal. In this case, it should show approximately 0.777777....

Step 4: Round to the Nearest Hundred Thousandth

The nearest hundred thousandth is the sixth digit after the decimal point. The original number from the calculator shows 0.777777.... To round, look at the seventh digit. Since it is 7 (which is greater than 5), you add 1 to the sixth digit, resulting in 0.77778.

Key Concepts

Using a Calculator for Division

Calculators are essential tools for performing arithmetic operations, including division, especially when dealing with decimals. They swiftly handle complex calculations that might be prone to errors if done manually. When dividing, identify the dividend and divisor—you input 7 as the dividend, and 9 as the divisor. Follow these steps to do the division:

• Turn on your calculator and enter the first number, 7.
• Press the division key, often represented by a '/'.
• Input the second number, 9, and press the equals key.

This sequence allows you to divide the numbers and receive an accurate result. Utilizing the calculator ensures speed and precision in determining that 7 divided by 9 equals approximately 0.777777.... Calculators save time and reduce computational errors.

Rounding Decimals Effectively

Rounding decimals is important when precise values are not necessary and to fit the level of accuracy required in specific scenarios. It involves adjusting a decimal number to a value that is easier to work with. To round to the nearest hundred thousandth:

• Locate the sixth digit after the decimal point. Here, it is the first '7' in 0.777777....
• Examine the seventh digit after the decimal point. In our case, it is also a '7'.
• If that digit is 5 or more, increase the sixth digit by 1. If it's less than 5, leave the sixth digit unchanged.

Since our seventh digit is a '7', which is greater than 5, we increase the sixth digit, leading us to 0.77778. This provides a clear, rounded result used in approximations while maintaining a fair degree of accuracy.

Steps to Successful Division

Understanding the steps to successful division helps break down the operation into manageable parts. Here’s how you can perform decimal division rigorously:

• Step 1: Identify your numbers—know your dividend and divisor. Example: 7 (dividend) divided by 9 (divisor).
• Step 2: Use a calculator to divide, to ensure you receive an accurate result. Here, the decimal result of 0.777777... is obtained.
• Step 3: Read the output on your calculator to ascertain the exact decimal.
• Step 4: Round the decimal to the required precision. Look closely at the digit to decide if the sixth place needs altering.

Following these steps methodically ensures a successful division calculation, whether you need the exact decimal or a rounded approximation, such as 0.77778, to tailor the output to your needs.