Question

The product of a number multiplied by 0.1 is 10 times as much as multiplying the same number by 0.01

Answer 1

The statement "The product of a number multiplied by 0.1 is 10 times as much as multiplying the same number by 0.01" is mathematically valid for all real numbers.

Let's denote the number as x. According to the given information:

The product of a number multiplied by 0.1 is 10 times as much as multiplying the same number by 0.01 can be mathematically expressed as:

0.1x = 10 × 0.01x

Let's solve this equation:

0.1x = 0.1x (Both sides are equal, which is true)

This equation holds for all real numbers x. Thus, it's a valid identity, indicating the statement is mathematically accurate.

Answer 2

The statement that the product of a number multiplied by 0.1 is 10 times as much as multiplying the same number by 0.01 is true

The analysis of the statement is as follows;

Let x represent the number, we get;

x × 0.1 = 10 × x × 0.01

10 × 0.01 = 0.1

Therefore, x × 0.1 = 0.1 × x

The statement is therefore true

The statement can also be proven using the location of the decimal point in 0.1 and 0.01, which indicates that the location of the number 1 in the decimal 0.1 is in the tenth place and the location of 1 in the decimal 0.01 is in the hundredth position, therefore, 0.1 is equivalent to the product between 10 and 0.01