Ahmed wrote two numbers. The first number has a 7 in its tenths place. The second number has a 7 with a value that is 1,000 times greater than the value of the 7 in the first number. In which place is the 7 in the second number?
The Correct Answer and Explanation is:
Correct Answer: Hundreds place
Explanation:
To solve this question, we need to understand place value—specifically how each digit in a number represents a different value depending on its position.
Step 1: Understand the 7 in the first number
The first number has a 7 in the tenths place.
A digit in the tenths place means it’s located just after the decimal point, like this:
- Example: 0.7 or 3.7 → Here, the 7 is in the tenths place.
The value of 7 in the tenths place is:
$$
7 \times \frac{1}{10} = 0.7
$$
Step 2: Multiply that value by 1,000
The problem states that the second number has a 7 whose value is 1,000 times greater than the 7 in the tenths place.
So we calculate:
$$
0.7 \times 1{,}000 = 700
$$
Now we need to ask: in what place would the digit 7 need to be to represent a value of 700?
Step 3: Identify the place of 7 that gives a value of 700
Let’s look at place values in whole numbers:
- Ones place: 7 → Value = 7
- Tens place: 7 → Value = 70
- Hundreds place: 7 → Value = 700
- Thousands place: 7 → Value = 7,000
Clearly, a 7 in the hundreds place gives a value of 700.
Conclusion:
So, the digit 7 in the second number must be in the hundreds place to have a value that is 1,000 times greater than the value of a 7 in the tenths place (0.7).
This question helps students apply their understanding of place value relationships—a fundamental math skill for comparing and understanding numbers.