Problem 86 - Prealgebra

Question

Compute the quotient 4/57, and round your answer to the nearest hundredth.

Step-by-Step Solution

Answer

0.07

Step 1: Setup the Division

To compute the quotient of 4 divided by 57, we start by setting up the division problem: \( \frac{4}{57} \).

Step 2: Perform the Division

Divide 4 by 57 using long division. This requires determining how many times 57 fits into 4, which is 0 times. So the division continues by considering more decimal places. The actual division yields approximately 0.0701754386.

Step 3: Round to the Nearest Hundredth

After performing the division, you get the result as a decimal. Look at the third decimal place to decide if you round up or down at the second decimal place. In this case, 0.0701754386 rounded to the nearest hundredth is 0.07.

Key Concepts

Understanding Long Division

Long division is a method used to divide larger numbers or ones not easily divisible by mental math. It helps break down a division problem step by step. In this exercise, we're dividing 4 by 57 using long division. First, you set up the division with 4 as the dividend (the number being divided) and 57 as the divisor (the number you are dividing by). Start by determining how many times 57 goes into the first digit of 4. Since 57 is larger than 4, you write a 0 to indicate it doesn’t fit. Next, you extend the division to include decimal places by appending zeros to the dividend, making it 4.0000 for further calculation. This process means repeatedly "borrowing" from the next decimal and checking how many times 57 fits into each accumulation. Through this method, you arrive at a quotient of approximately 0.0701754386.

Role of Decimal Places in Division

Decimal places come into play when you can't divide a number evenly. They allow you to continue dividing past the whole numbers into the tenths, hundredths, thousandths, and so on. In our problem, since 4 cannot be divisible by 57 in even whole numbers, we use decimal places. We transform the initial whole number division into one with decimal places by imagining 4 as 4.0000. This technique gives more precision to your quotient, enabling you to reach an answer that reflects the true value of the division as closely as possible. Remember, the more decimal places you consider, the more precise your answer will be, especially important in scientific calculations. However, often you only need to find and use a specific number of decimal places, like in this case, a consistent look at tenths and hundredths.

Rounding Numbers to the Nearest Hundredth

Rounding involves making a number simpler while keeping it close to the original amount. It's handy when you need a more digestible number. To round to the nearest hundredth, you look at the third decimal place: hundredths involve two decimal spots, so the third digit determines rounding. In our exercise, the result of long division was about 0.0701754386. To round this to the nearest hundredth, you examine the digit in the thousandth's place (the third decimal place), which is 1. Since 1 is less than 5, we don't round up, leaving the hundredth value as it is. Hence in our example, 0.0701754386 rounded to the nearest hundredth is 0.07. This process ensures the precision is suitable for most educational and practical purposes while maintaining simplicity in use.