Problem 77 - Prealgebra

Question

Compute the quotient \(52 / 83\), and round your answer to the nearest tenth.

Step-by-Step Solution

Answer

0.6

Step 1: Set up the division

Write the division problem with 52 as the dividend and 83 as the divisor: \(52 \div 83\).

Step 2: Perform the division

Perform the division using long division until you get a sufficient number of decimal places to round to the nearest tenth. The division yields approximately 0.6265.

Step 3: Round to the nearest tenth

Look at the hundredths place (2nd decimal place) in the result 0.6265, which is 2. Since it is less than 5, round down, keeping the tenths place the same. Therefore, 0.6265 rounds to 0.6.

Key Concepts

Rounding

Rounding is a technique used to simplify a number by reducing the digits, yet keeping the number close to its original value. Imagine you have a number with multiple decimal places, and you want to make it simpler by keeping only a certain number of necessary decimals.
This is where rounding comes in handy! When rounding a decimal number to the nearest tenth, you focus on the digits in the tenths and hundredths places:

• Look at the tenths (first decimal) and the hundredths (second decimal) places.
• If the digit in the hundredths place is 5 or more, round up the digit in the tenths place by one.
• If the digit in the hundredths place is less than 5, keep the tenths place digit as is.

For instance, when rounding 0.6265 to the nearest tenth, check the hundredths place, which is 2. As 2 is less than 5, the number rounds to 0.6. Rounding is an essential skill in math because it helps in estimation and making numbers easier to work with in daily calculations.

Decimals

Decimals are numbers containing a decimal point to represent a fraction of a whole. They offer a way of expressing non-whole numbers in terms of powers of ten. For instance: 0.1 is one-tenth, 0.01 is one-hundredth. In long division, result can often be a decimal, especially if the divisor does not perfectly divide the dividend. When working with decimals, understanding their place value is crucial:

• The first digit to the right of the decimal point is in the tenths place.
• The second digit is in the hundredths place.
• The third digit is in the thousandths place, and it continues in this pattern.

Decimals are quite flexible and enable precise calculations in various fields, from finance to science. Hence, understanding decimals well will help you navigate both academic and real-world mathematical problems.

Long Division

Long division is a method used to divide larger numbers by breaking the division process down into easier steps. This traditional technique helps solve division problems, especially when dealing with large numbers or when the division results in decimals.To perform long division in a problem like \(52 \div 83\), follow these steps:

• Estimate how many times 83 can fit into 520 (since 83 doesn't fit into 52, you include a zero and consider 520).
• Calculate and multiply to see how many whole times 83 fits, adjusting if needed.
• Bring down digits as necessary to continue the division.
• Once the division reaches a satisfying decimal length, you stop.

The use of long division becomes essential when the quotient (the result of division) includes decimals. It does not only give the exact quotient but also helps in understanding how division extends into decimals. With practice, long division becomes a powerful tool for finding both exact and approximate results.