Write an expression for the amount of money (in dimes) in n dollars

Write an expression for the amount of money (in dimes) in n dollars.

The correct answer and explanation is:

Answer:
The amount of money in dimes for nn dollars is: 10n\boxed{10n}

Explanation:

To understand why the expression for the amount of money in dimes for nn dollars is 10n10n, we need to break down the problem step-by-step.

1. Understanding the Units:
   • A dollar is a unit of currency.
   • A dime is a coin worth 10 cents.
   • There are 100 cents in 1 dollar.
   • Since each dime is worth 10 cents, there are 10 dimes in one dollar because 100 cents10 cents per dime=10\frac{100 \text{ cents}}{10 \text{ cents per dime}} = 10.
2. Relating Dollars to Dimes:
   • If 1 dollar equals 10 dimes, then nn dollars would equal 10×n10 \times n dimes.
   • This is a simple multiplication because the number of dimes is directly proportional to the number of dollars.
3. Forming the Expression:
   • Let nn represent the number of dollars.
   • Then the total number of dimes can be expressed as: number of dimes=10×n=10n\text{number of dimes} = 10 \times n = 10n
4. Example:
   • If you have 5 dollars, how many dimes is that?
   • Using the formula 10n10n, substitute n=5n = 5: 10×5=50 dimes10 \times 5 = 50 \text{ dimes}
   • This matches what we expect: 5 dollars is the same as 50 dimes.
5. Importance of this Expression:
   • It helps convert between different units of currency, useful in many real-life situations like counting coins.
   • It simplifies calculations without having to manually count each dime or convert cents repeatedly.

In conclusion, the key to the expression is recognizing that each dollar contains exactly 10 dimes. Multiplying the number of dollars by 10 gives the total number of dimes, making the expression 10n10n both simple and accurate.