Problem 87 - Prealgebra

Question

Compute the quotient \(16 / 86\), and round your answer to the nearest tenth.

Step-by-Step Solution

Answer

The quotient is approximately 0.2.

Step 1: Set Up the Division

We are given the problem to compute \(16 \div 86\). This means we want to find out how many times 86 can go into 16 when expressed as a decimal.

Step 2: Perform the Division

Divide 16 by 86. This involves long division. 16 is smaller than 86, so the integer part of the quotient is 0, and we continue with decimal division. 16 divided by 86 gives us approximately 0.186.

Step 3: Round to the Nearest Tenth

Look at the result of 0.186. The tenths place is 1, and the hundredths place is 8. Since 8 is greater than or equal to 5, we round up. Therefore, 0.186 rounded to the nearest tenth is 0.2.

Key Concepts

Decimal Division

Decimal division is a method used when you divide numbers and at least one of them is a decimal or when the result is a decimal. In the case of dividing 16 by 86, we find that 16 is too small to be divided whole by 86. Hence, we switch to decimal division. The quotient here turns less than 1, which means the result will appear after the decimal point. This process helps in precisely calculating parts of a whole.

• Start by placing a decimal point in the quotient, following with zeros or more digits as needed.
• Bring down digits one-by-one from the dividend (16 here) to divide by the divisor (86).
• Estimations and careful calculations are crucial to ensure accuracy in the division.

Rounding

Rounding is the process of approximating a number to make it simpler while keeping its value close to the original number. In our problem, after performing decimal division, we need to round the quotient. The unrounded decimal 0.186 has digits beyond the tenths place. To complete rounding, we follow these steps:

• Identify the digit in the place you are rounding to—in this case, the tenths place, which is 1.
• Look at the next digit to the right, which is 8 in the hundredths place.
• If this next digit is 5 or more, increase the tenths place by 1; if not, it stays the same.
• Therefore, 0.186 rounds up to 0.2, as 8 is greater than 5.

Long Division

Long division is a traditional method of dividing one number by another to find a quotient. It's essential when dealing with larger numbers or when the division isn't straightforward. Performing long division requires a clear process and precision. Here's how it works for dividing 16 by 86:

• Begin by writing 16 under the division bracket and 86 outside.
• As 86 doesn't fit into 16, start with 0 and begin after the decimal point.
• Introduce zeros to 16, making it 160 and so on to see how many times 86 fits into each new number.
• Subtract the product from your number and bring down the next digit.
• Continue this process until you've divided the entire number or reached the desired decimal termination.

Understanding long division helps see exactly how the division process unfolds and is particularly useful when performing decimal division or rounding.