Multiplying decimals

As I said yesterday, today we’re looking at multiplying decimals and the sort of wacky rules it plays by.

Remember on Monday when I said decimals can be represented as fractions? Let’s start by reviewing what happens when we multiply fractions. It’s important to understand something that happens when we multiply decimals.

Let’s say we want to multiply 16.53 and 4.07. Remember that 0.53 is really 53/100 and 0.07 is really 7/100. If we multiplied these two fractions together, we’d end up with a denominator of 10,000.

If we multiply 16.53 and 4.07 together, we don’t actually line up the decimal points. We line up the far right numbers.

Correct: 16.53                                 Incorrect: 16.53

              * 4.07                                                 * 4.07

              ———–                                                 ———-

 

We then multiply the numbers as if they were really 1,653 and 407, giving us an answer of 672,771. But we still have that decimal point to place. Above, I said multiplying the fractions would give us a denominator of 10,000, which says this number would end in the ten-thousandths. That means it would end four places after the decimal point, and would become 67.2771.

You could also remember this little shortcut: Count up how many numbers are to the right of all the decimal points, and then count that many numbers from the right in the answer.

Tomorrow, we should be taking a look at dividing decimals.

Adding and subtracting decimals

Continuing on our theme of decimals, today let’s look at adding and subtracting them.

If you know how to add and subtract whole numbers, then adding and subtracting decimals will be simple. The most important thing to remember when adding and subtracting decimals is that you must line up the decimal points when you write the problem vertically. It’s like normal addition and subraction; you’re aiming to line up the place values.

Correct:  16.85                                                   Incorrect: 16.85

              -  4.91                                                                   – 4.91

                ———-                                                                  ———–

The normal rules about carrying and borrowing apply when you’re adding and subtracting decimals. The above problem, when worked correctly, will involve the 8 borrowing from the 6, and will give us back an answer of 11.94. The decimal point stays lined up with the other numbers in the problem.

Tomorrow, we’ll look at multiplying decimals, which plays by different rules.

What is a decimal?

Like the fraction, a decimal is just part of a number. In fact, we can represent a decimal as a fraction. For example, seven tenths can be represented in decimal form as 0.7 and in fraction form as 7/10. Both represent the exact same value.

Unlike fractions, though, decimals have a set of very specific names based on place value: tenths, hundredths, thousandths, etc. Fractions can be halves, thirds, fourths, thirty-sevenths, etc. We name decimals by saying the number represented and the place value of the digit farthest to the right. For example, 0.82 is read as “eighty-two hundredths”. 1.387 would be read as “one and three hundred eighty-seven thousandths”.

All decimals can be rewritten in fraction form (this is sometimes easier when working certain problems). You simply write the number in the numerator and the place value in the denominator. For example, 0.67 (sixty-seven hundredths) becomes 67/100. 2.45 becomes 2 45/100. Then, you reduce the fraction is necessary or possible. In the second example, the fraction simplifies, leaving us with 2 9/20.

Decimals aren’t any more scary than fractions. Just remember they’re just part of a number.