Final answer:
To create decimal numbers with an even number in the tenths place, an odd number in the hundredths place, and a prime number in the thousandths place, we utilize our knowledge of integer powers of ten and the properties of even, odd, and prime numbers. Examples include 0.462, 0.273, 0.584, and 0.695.
Step-by-step explanation:
The student has asked us to write four decimal numbers that meet specific criteria in different decimal places: an even number in the tenths place, an odd number in the hundredths place, and a prime number in the thousandths place. To better understand decimal places, we can refer to the concept of integer powers of ten. For example, 103 represents 1,000 while 10-4 represents 0.0001. To multiply by powers of ten, we can move the decimal point to the right by the number of zeros in the power of ten.
When constructing our numbers, we first need to recognize which numbers are considered even, odd, and prime. Even numbers are divisible by 2, odd numbers are not divisible by 2, and prime numbers are those greater than 1 that have no divisors other than 1 and themselves. For the thousandths place, prime numbers we can use include 2, 3, 5, and 7. Given these criteria, some examples of numbers that fit the requirements are:
- 0.462 (even=4, odd=6, prime=2)
- 0.273 (even=2, odd=7, prime=3)
- 0.584 (even=8, odd=4, prime=4)
- 0.695 (even=6, odd=9, prime=5)
These examples demonstrate how we can construct numbers to meet specific criteria in their decimal places by understanding the concept of integers and powers of ten.