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Chapter 5: Problem 568

In the following exercises, divide. $$ 0.48 \div 6 $$

Short Answer

Expert verified
0.08

Step by step solution

01

Set up the division

Write the problem in long division format: \[ 0.48 \text{ divided by } 6 \text{ or } \frac{0.48}{6} \]
02

Move the decimal point

To make the division simpler, move the decimal point in 0.48 two places to the right to get 48. Similarly, move the decimal point in 6 two places to the right, giving 600. The new equation is now \( \frac{48}{600} \).
03

Divide the numbers

Now, divide 48 by 600 using long division. Perform the division step by step as follows:48 goes into 600 0 times.Therefore, place 0 before the decimal point and continue with 48.48 goes into 6000 (600 shifted to the right) approximately 0.08 times.So, \( \frac{48}{600} = 0.08 \).
04

Place the decimal point

Finally, place the decimal point correctly in the result. Since the original divisor was 6, the decimal should be two places to the left in the quotient. Therefore, the final result is 0.08.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Long Division
Long division is a method used to divide large numbers, step-by-step. We write the divisor outside the division bracket and the dividend inside it. Then, we repeatedly determine how many times the divisor fits into various segments of the dividend. This old-school technique breaks down complex division problems into simpler tasks. When dividing decimals, follow the same steps as whole numbers but pay special attention to where the decimal point goes.
Decimal Point
The decimal point separates the whole number part from the fractional part of a number. In decimal division, it's crucial to adjust the position of the decimal point correctly.
Let's look at an example with the problem \(\frac{0.48}{6}\). We need to move the decimal point in 0.48 two places to the right, making it 48. Similarly, move the decimal point in 6 two places to the right, turning it into 600. Now, the division problem is \(\frac{48}{600}\). Moving the decimal points helps in simplifying the division.
Division Process
To start the division process, align your numbers and place them correctly within and outside the division bracket. Divide the modified numerator by the modified denominator.
For example, with \(\frac{48}{600}\), evaluate how many times 48 fits into 6000 (since we moved decimals two places, we consider 6000 instead of 600). The result is approximately 0.08.
Next, position the decimal point in the quotient correctly. If we adjust two decimal places to the right in the dividend and divisor, the final result remains at the same precision. So, \(\frac{0.48}{6} = 0.08\). Remember, precision and careful decimal management are vital in the division process.

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