Problem 78 - Prealgebra

Question

Compute the quotient \(43 / 82\), and round your answer to the nearest tenth.

Step-by-Step Solution

Answer

The quotient is approximately 0.5.

Step 1: Understand the Problem

The problem asks us to find the quotient of 43 divided by 82 and then round the result to the nearest tenth.

Step 2: Perform Division

Divide 43 by 82 to obtain a decimal. Use long division or a calculator to find that \[\frac{43}{82} \approx 0.5244\]

Step 3: Round the Quotient

Look at the hundredths place in 0.5244, which is 2. Since it is less than 5, we round down to the nearest tenth. This means the number rounded to the nearest tenth is 0.5.

Key Concepts

Rounding Decimals

Rounding decimals is an essential skill, especially when you need to provide a cleaner, more understandable number. To round a decimal, you must look at the digit in the place immediately after your desired rounding place. In this context, rounding to the nearest tenth, we're focused on the digit in the hundredths place.
If the hundredths place is 5 or more, it means rounding up. Conversely, if it's less than 5, you round down.
For example, in the decimal 0.5244, the digit in the hundredths place is 2. Since 2 is less than 5, when rounding to the nearest tenth, you round down to 0.5.
Understanding where to round and how it affects your final result is crucial for accurate solutions. It helps in approximating numbers in calculations, making them easier to understand and communicate.

Quotient Calculation

The quotient is the result of a division problem and represents how many times one number can fit into another. In basic arithmetic, the division is represented as: \[\text{Dividend} \div \text{Divisor} = \text{Quotient}\]For the given problem, we divided 43 by 82. Using either a calculator or a manual method, like long division, we found the quotient: approximately 0.5244.
The process can be visualized as trying to distribute 43 into 82 equal parts, which, as expected, results in a smaller value less than 1, because the dividend is less than the divisor. Knowing how to calculate a quotient is fundamental in division operations and helps in numerous mathematical applications, such as fractions, ratios, and real-world problem-solving scenarios.

Long Division

Long division is a systematic way of dividing complex numbers without a calculator. It involves a series of steps that simplify a division problem into manageable parts.

• First, set up the division by placing the divisor (82) outside the division bracket and the dividend (43) inside.
• Next, determine how many times the divisor fits into the leading digits of the dividend. Since 82 is greater than 43, look for a multiple of 10 by appending a decimal point and zeroes to 43.
• Subtract the product from the dividend to get a new number, and bring down the next digit if available.

This continues until you've divided as much as you need to complete the calculation to your required precision.
Whether using it as a primary method or checking work from other tools, long division provides clarity on every step, ensuring solid understanding of division mechanics.