# Decimals

In this unit you’ll learn how to do everything with decimals.

Multiplying Decimals- When you multiply decimals, you multiply as if there are no decimals, but you remember how many numbers are behind the decimal. In the problem 1.7 x 2.9, there are two numbers behind the decimal. After you remember how many numbers are behind the decimal, multiply like normal to get your product of 493. Since there was two numbers behind the decimal, make sure your product has two numbers behind the decimal. So in all, your product would be 4.93 because two numbers are behind the decimal.

Place Value Decimals-  When you do place value with decimals, you always end in -ths. Since decimals are not whole numbers and are fractions, you can not end in a -s, and therefore, you have to end in -ths. The 1st number behind the decimal is the tenths, the 2nd is the hundredths, the 3rd is the thousandths, and so on. When you say a number that has a decimal, you say the whole number, and then you say “and”, referring to the decimal, and after that you say the numbers behind the decimal and their place value. For instance, when you say 3.456, you would say ” 3 and 456 thousandths”.

Expanded Form Decimals- When you do expanded form with decimals, you break the number apart. When you do expanded form with the number 789.665, you split it like this: 700+80+9+0.6+0.06+0.005=789.665.

Non-Allined Decimals- When you have non-allined decimals, line up the decimals vertically first.

Fractions to Decimals- To turn a fraction into a decimal, divide the numerator by the denominator. To learn more about fractions, visit the fractions unit.

Dividing with Decimals- If the divisor has a decimal in it, multiply it so there is no decimal. And remember: what you do to one you do to the other. In the problem 2.4 divided by .5, multiply .5 by 10 to get 5. And since you do the same thing to the other one, multiply 2.4 by 10 to get 24. Then divide 24 by 5 to get your product of 4.8.

Dividing the Remainder- When you divide the remainder, you have to remember that every number has an understood decimal at the end. When you divide 24 by 5, you have to divide the remainder. The first step in this problem is to multiply 5 by 4 to get 20. Then you bring your 4 above the top line and then subtract 20 from 24 to get 4. Instead of stopping there, bring up your decimal and bring down your zero that was after your decimal to get a total of 40. Then you can multiply 5 by 8 to get 40, bring the 8 up and put it behind the decimal, and subtract 40 from 40 to get your answer of 4.8.