Question

Will the product of 22.65 × 0.999 be greater than or less than 22.65? Without calculating, explain how you know.

Answer 1

Answer:

It will be less

Step-by-step explanation:

logically as common knowledge, it's a decimal so it'll be a little bit less

Answer 2

The product of 22.65 × 0.999 will be less than 22.65. The reason is because the second multiplicand is smaller than 1.

See below for explanation.

Given that:

The product is 22.65 × 0.999

It is to be decided whether this product is less or greater than 22.65 without actual multiplication.

Explanation:

In positive real numbers multiplication, suppose we have $a \times b$

If suppose b is less than 1 then we can say symbolically:

$b < 1$

Now multiplying a both sides, we get:

$a \times b < a \times 1\\a \times b < a$

Thus, from the same concept, we have:

$0.999 < 1\\22.65 \times 0.999 < 22.65 \times 1\\22.65 \times 0.999 < 22.65$

This all can be done in mind, it is because it is a basic conclusion in mathematics that if you multiply a number with something smaller than 1, then that number's magnitude will decrease.

Thus, since 0.999 is less than 1, when we multiply it with a positive number 22.65, the number 22.65 will become less than itself.

Learn more about multiplication and comparison here:

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