Answer :
To determine which digits all multiples of 5 end with, we can look at what happens when we multiply various whole numbers by 5.
When you multiply any number by 5, the result is dependent on the digit you are multiplying. However, regardless of the whole number being multiplied, there are some consistent patterns observed in the units place (also known as the ones place) when considering multiples of 5.
Let's consider the multiplication sequence of 5:
- 1 × 5 = 5
- 2 × 5 = 10
- 3 × 5 = 15
- 4 × 5 = 20
- 5 × 5 = 25
- 6 × 5 = 30
- 7 × 5 = 35
- 8 × 5 = 40
- 9 × 5 = 45
- 10 × 5 = 50
Looking at this sequence, we can observe that all multiples of 5 end in either a 0 or a 5. This pattern continues indefinitely:
- Any even number multiplied by 5 will end in a 0.
- Any odd number multiplied by 5 will end in a 5.
This is because the product of an even number and 5 will be an even number and, hence, might be expressed as 10n, which always ends in 0. On the other hand, the product of an odd number and 5 will be "5 more" than an even multiple of 10, and hence will always end in a 5.
Because this pattern of ending with a 0 or a 5 is uniform for all whole number multiples of 5, we can conclude that all multiples of 5 will end with the digits 0 or 5.
When you multiply any number by 5, the result is dependent on the digit you are multiplying. However, regardless of the whole number being multiplied, there are some consistent patterns observed in the units place (also known as the ones place) when considering multiples of 5.
Let's consider the multiplication sequence of 5:
- 1 × 5 = 5
- 2 × 5 = 10
- 3 × 5 = 15
- 4 × 5 = 20
- 5 × 5 = 25
- 6 × 5 = 30
- 7 × 5 = 35
- 8 × 5 = 40
- 9 × 5 = 45
- 10 × 5 = 50
Looking at this sequence, we can observe that all multiples of 5 end in either a 0 or a 5. This pattern continues indefinitely:
- Any even number multiplied by 5 will end in a 0.
- Any odd number multiplied by 5 will end in a 5.
This is because the product of an even number and 5 will be an even number and, hence, might be expressed as 10n, which always ends in 0. On the other hand, the product of an odd number and 5 will be "5 more" than an even multiple of 10, and hence will always end in a 5.
Because this pattern of ending with a 0 or a 5 is uniform for all whole number multiples of 5, we can conclude that all multiples of 5 will end with the digits 0 or 5.
