Problem 42 - Prealgebra

Question

Carry out cach of the following divisions only so far as needed to round the results to the nearest hundredth. $$0.99 \div 0.5$$

Step-by-Step Solution

Answer

0.99 divided by 0.5 equals 1.98, rounded to the nearest hundredth.

Step 1: Understanding the Problem

We need to divide 0.99 by 0.5 and round the result to the nearest hundredth. This means we will perform the division and then adjust the resulting number to two decimal places.

Step 2: Perform the Division

Divide 0.99 by 0.5. Perform the division by multiplying both numbers by 10 to eliminate the decimal in 0.5, which simplifies the problem to dividing 9.9 by 5.

Step 3: Calculate the Quotient

Divide 9.9 by 5. This gives us 1.98 as the result without rounding. We can do this by setting up the division as long division or using a calculator for more precision.

Step 4: Rounding the Result

Since the quotient 1.98 is already in the format of the hundredth place, and it does not require further rounding, we can finalize this as the rounded result.

Key Concepts

Understanding Rounding Decimals

Rounding decimal numbers is a useful skill when you want to simplify a number without significantly changing its value. The goal is to limit the decimal to a certain number of places, like the nearest whole number, tenth, or in this case, the hundredth place. When rounding to the nearest hundredth:

• Look at the digit in the thousandths place, which is the third digit to the right of the decimal point.
• If this digit is 5 or greater, increase the hundredths digit by 1.
• If it's less than 5, keep the hundredths digit the same.

In our example, the division of 0.99 by 0.5 gives us 1.98. Since there are only two digits after the decimal point, there's no further digit to check, meaning 1.98 is already rounded to the nearest hundredth.

Mastering Long Division with Decimals

Long division can be a little tricky, but it's a powerful method to understand what happens when dividing decimals. To divide by a decimal:

• Convert the divisor to a whole number by multiplying it by 10 (or 100, etc., depending on the number of decimal places).
• Remember to do the same to the dividend for balance.

For example, when dividing 0.99 by 0.5:

• Multiply both numbers by 10 to shift the decimal point, transforming the problem into 9.9 divided by 5.

Now perform the division as if you're handling whole numbers. Set it up as traditional long division where you:

• See how many times the divisor (5) fits into sections of the dividend (9.9).
• Subtract the product from the relevant figures in the dividend, bringing down the next digits as you go.

This way, we discover that 9.9 divided by 5 is exactly 1.98.

Unpacking the Role of Quotients

A quotient is simply the result of division. It tells us how many times one number is contained within another. Here, the task is to find the quotient of 0.99 and 0.5. In decimal division, decimal points in the divisor can complicate things. That's why we adjust them for easier computation. - By converting 0.5 into a whole number (5), and similarly adjusting the dividend, we clarify the process. - After performing the division, the quotient of 9.9 by 5 is 1.98, a result already expressed to the nearest hundredth. So, the quotient you find in a division problem isn't just a number. It represents a part of the whole. By ensuring it's in the simplest, most precise form possible (like rounding), you get a clearer understanding and easily communicated result.