Can the product of two decimals be a natural number?

Question

Homi · Accepted Answer

We need to see if multiplying two decimal numbers can result in a whole number.

Step 1 — What are these numbers?

Let us first understand natural numbers. Natural numbers are counting numbers. They are $\mathbf{1, 2, 3, 4}$ , and so on. They do not have any decimal part.

Now, let us understand decimal numbers. Decimal numbers have a decimal point. Examples are $\mathbf{0.5}$ , $\mathbf{1.25}$ , or $\mathbf{3.0}$ . A number like $\mathbf{3.0}$ is also a natural number. But we are looking for two decimals. Let us choose decimals that are not natural numbers.

Step 2 — Finding an example

We need to find two decimal numbers. Let us call them Decimal 1 and Decimal 2. Their product must be a natural number. Let us try Decimal 1 as $\mathbf{1.25}$ . Let us try Decimal 2 as $\mathbf{0.8}$ . We will multiply these two decimals. First, we can write them as fractions. $\mathbf{1.25}$ is the same as $\mathbf{125/100}$ . This fraction can be simplified. $125/100$ $= 5/4$ Next, $\mathbf{0.8}$ is the same as $\mathbf{8/10}$ . This fraction can also be simplified. $8/10$ $= 4/5$ Now, we multiply these two fractions. We multiply the numerators together. We multiply the denominators together. $(5/4) \times (4/5)$ $= (5 \times 4) / (4 \times 5)$ $= 20 / 20$ $= 1$ The product is $\mathbf{1}$ . $\mathbf{1}$ is a natural number. So, the product of $\mathbf{1.25}$ and $\mathbf{0.8}$ is a natural number.

$\boxed{\text{Yes, the product can be a natural number.}}$

Answer

(i) Yes.

Question 5

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