Why isn't decimal numbers aligned when multiplying decimals?

Answer 1

When multiplying decimals, the decimal points are not only not aligned they are completely removed from the numbers to leave a multiplication of whole numbers which is done.

Then the decimal point is put back into the answer by counting how many digits in total were after the decimal points in the original numbers and making the answer have the same number of digits after the decimal point.

Example:

1.23 x 45.6 → 123 x 456 = 56088

1.23 has 2 digits after the decimal point,

45.6 has 1 digit after the decimal point

making a total of 2 + 1 = 3 digits after the decimal point in the question, so there must be 3 digits after the decimal point in the answer

→ 1.23 x 45.6 = 56.088

Second example:

1.25 x 3.4 → 125 x 34 = 4250

2 digits + 1 digit = 3 digits in total in question must be after decimal point in answer:

→ 1.25 x 3.4 = 4.250

but normally any zeros that come at the end of a number after a decimal point are not written, so this would normally be written as:

1.25 x 3.4 = 4.25

A decimal number is a whole number divided by a power of 10, that is 10, 100, 1000, etc.

This means that a decimal number can be written as an improper fraction with a power of 10 as the bottom number.

So for the first example:

1.23 = 123/100

45.6 = 456/10

Multiplying the decimals together is the same as multiplying the two fractions together, which is done by multiplying the top numbers together and multiplying the bottom numbers together:

1.23 x 45.6 = 123/100 x 456/10

= (123 x 456)/(100 x 10)

= 56088/1000

= 56.088