Multiplying/ Dividing with Decimals

Understanding Decimal Numbers

Decimal numbers are a system of numbers that includes a decimal point and the numbers that follow it, representing fractions of a whole number.
The value of a digit after the decimal point decreases by a factor of ten for each position to the right. For instance, in the number 1.23, the 2 represents 2 tenths and the 3 represents 3 hundredths.

To multiply decimal numbers, ignore the decimal point at first and carry out the multiplication as if you were dealing with whole numbers.
Once you’ve multiplied the numbers, count the total number of digits that are after the decimal points in the original numbers. The product should also have this many digits after its decimal point.
If the total number of digits after decimal points in your answer is fewer than you need, add zeroes to the start of your answer (to the left of existing digits). If there are more, you have likely made an error.
For example, if we multiply 0.5 by 0.4, we think of it as 5 times 4 (which is 20) and then ensure the product also has two digits after the decimal point, giving 0.20 (which is usually written as just 0.2).

When dividing with a decimal number, you can transform the division problem into a easier one involving whole numbers only.
To do this, shift the decimal point in both the number you’re dividing (the dividend) and the number you’re dividing by (the divisor) the same number of places to the right until the divisor becomes a whole number.
For example, if you’re dividing 5.6 by 0.7, you would shift the decimal point one place right in each number, turning the problem into 56 divided by 7.
Once you have turned it into a whole number problem, perform the division as usual.

Ignorance of decimal placement, especially in multiplication, can easily lead to incorrect answers. For example, 0.4 multiplied by 0.3 is 0.12, not 1.2.
When converting a division problem involving decimal numbers to a whole number problem, it’s crucial to shift the decimal point in both the dividend and divisor equally. Unequal shifts can cause significant errors.
It is common for people to forget about leading zeros when counting the number of digits after the decimal point. Always remember to count the place value of the digits in decimal fractions. For example, 0.02 has two digits after the decimal point, not one.
In division, rounding your answer too early can cause significant mistakes. If your answer doesn’t divide evenly, keep a few extra decimal places in your intermediate steps to ensure accuracy. Only round the final result.