which number when multiplied by 5 gives products having 5 at the units place?
Answers
all odd no. when multiplied by 5 gives product having 5 at units place
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To find :
A number which gives 5 as a product in the units place, when multiplied by 5.
Solution :
• There are two types of natural numbers, odd and even. Let us check by taking each type at once.
(i) By taking odd numbers first :
For say, let us take 1 and multiply it by 5. The product is 5, satisfying the condition of having 5 in the units place.
• Let us take another random 2-digit odd number, say 11. Multiplication of 11 by 5 gives 55 as the product, again, having 5 in the units place.
• Checking a 3-digit negative odd number, like - 123, also gives 5 in the units place on being multiplied by 5, the product being - 615.
• It can therefore, be concluded that all odd numbers give 5 in the units place, when multiplied by 5.
(ii) Let us now check with even numbers :
• Multiplying the even number 2 by 5 gives 10 as the product, which clearly shows that 5 is not the digit in the units place.
• Therefore, we need not check further to conclude that an even number does not give 5 in the units place on being multiplied by 5.
• Now, in general, an odd number can be represented as 2n + 1, where n = whole number ranging from - ∞ to + ∞ .
Therefore, every odd number of the form 2n + 1 has 5 as a product in the units place, when multiplied by 5.