To solve the division problem of 9.69 divided by 0.38, we can follow the standard procedure for dividing decimal numbers. First, we will move the decimal point in the divisor (0.38) to the right until we have a whole number, and then move the decimal point in the dividend (9.69) the same number of places to the right. This will allow us to perform the division as if we were dividing whole numbers.
Step-by-Step Division Process
We start with 0.38 and move the decimal point two places to the right to get 38. Since we moved the decimal point two places in the divisor, we must also move the decimal point in the dividend (9.69) two places to the right, resulting in 969. Now, we can proceed with the division as follows: 969 divided by 38.
Performing the Division
The division of 969 by 38 can be performed using long division or a calculator. Performing the long division, we find that 38 goes into 969 approximately 25.5 times. However, since we are looking for a precise result and we initially moved the decimal point two places to the right, we need to move the decimal point in our result two places to the left to account for this adjustment.
The precise calculation is as follows: 969 ÷ 38 = 25.5. Since we adjusted the decimal point two places to the right initially, our actual result for 9.69 divided by 0.38 is 25.5.
| Operation | Result |
|---|---|
| 9.69 divided by 0.38 | 25.5 |
Understanding Decimal Division
Decimal division involves dividing a number by a decimal value. This operation is common in various mathematical and real-world applications, such as calculating percentages, ratios, and proportions. Understanding how to perform decimal division accurately is crucial for solving problems in finance, science, and engineering.
Real-World Applications
Decimal division has numerous practical applications. For instance, in finance, it can be used to calculate the cost per unit of an item when buying in bulk. In science, it helps in determining the concentration of a substance in a solution. In everyday life, decimal division can be used to split bills, calculate tips, or determine the price per ounce of a product.
In the context of the problem 9.69 divided by 0.38, if we were calculating the cost per unit, where 9.69 represents the total cost and 0.38 represents the quantity per unit, the result (25.5) would indicate the cost per unit of the item in question.
What is the general rule for dividing by decimals?
+The general rule is to move the decimal point in the divisor to the right until you have a whole number, and then move the decimal point in the dividend the same number of places to the right. After performing the division, adjust the result by moving the decimal point to the left by the same number of places it was moved in the dividend.
How does decimal division apply to real-world scenarios?
+Decimal division applies to various real-world scenarios, including finance (calculating costs per unit, percentages), science (determining concentrations), and everyday life (splitting bills, calculating prices per unit). It’s essential for accurately solving problems that involve ratios, proportions, and percentages.
