Problem 85 - Prealgebra

Question

Compute the quotient \(7 / 72\), and round your answer to the nearest hundredth.

Step-by-Step Solution

Answer

The rounded quotient of 7 divided by 72 is 0.10.

Step 1: Understand the Problem

We need to compute the division of two numbers: 7 and 72. Then, we must round the result to the nearest hundredth.

Step 2: Perform the Division

Calculate the division of 7 by 72 using long division or a calculator. This results in a decimal number approximately 0.097222... .

Step 3: Round to the Nearest Hundredth

To round the result from Step 2 to the nearest hundredth, look at the thousandth place (the third digit after the decimal point). The number in the thousandth place is 7, which is 5 or more. Therefore, we round up the number in the hundredth place from 9 to 10. However, since 9.10 isn't correct, it actually becomes 0.10 after rounding.

Key Concepts

Long Division

Long division is like a step-by-step method that helps us divide complex numbers. It breaks down the division into smaller, more manageable parts.
For our example, we have to divide 7 by 72. Here's a simple way to look at it:

• Set up 7 as the dividend and 72 as the divisor.
• Since 72 is larger than 7, 72 goes into 7 zero times initially. So, we start by noting that our integer part is zero.
• Extend the division into decimals by adding zeros to 7, making it 70, then 700, and so on, until the divisor fits.
• We find that 72 fits into 700 nine times, giving us 648, which leaves a remainder of 52.
• Continue this process, bringing down more zeros, until the desired decimal places are found.

This repetitive process helps in finding the quotient to as many decimal places as needed.

Rounding Decimals

Rounding decimals is an essential skill in mathematics when you want to approximate a number to make it easier to read or work with.
The process involves looking at the decimal places and deciding which number to round to, based on the digits that follow.

• Identify the place value you need to round to. In the context of this problem, it's the hundredths place – the second digit after the decimal point.
• Next, look at the digit immediately following the desired place value (the thousandths place in our case).
• If this digit is 5 or above, round the target digit up by one. If it's below 5, leave the target digit as is.

By rounding our division result of 0.097222... to the nearest hundredth, we observed and utilized this exact process.

Nearest Hundredth

Rounding a number to the nearest hundredth means making sure the number only has two digits after the decimal point. It's like saying, "I want my measurement to be precise to one cent in terms of money."
When you look at a number like 0.097222..., rounding to the nearest hundredth involves:

• Focusing on the hundredths place (the second decimal place), which is 9 in our example.
• Looking at the thousandths place (the third decimal place) to decide if rounding up is necessary.
• Since the thousandths place is 7, which is 5 or more, the rule is to add one to the hundredths place number 9, resulting in 10.
• This increases the integer part forward, transforming 0.099... into exactly 0.10 after rounding.

This approach makes it clear and simple to round decimals accurately.