Decimals are very similar to fractions. The difference is that the denominators are only the numbers 10, 100, 1000, etc, and we use a period (.) as a point to seperate the decimal numbers from any whole numbers to the left of the decimal point.

For example, the decimal for 1/10 is written .1 and said to be “point” one. (notice the “1” is to the right of the decimal point!)

We also can say .1 is one-tenth.

What this means is .1 is one-tenth of something or 1 piece out out 10 pieces. It also means one thing divided or broken into ten pieces…and .1 is one of those pieces.

Another example, let’s say we have a candy bar and we break it into 10 pieces. Each of the pieces is .1 of the candy bar. And if you are given 2 pieces out of the 10, you’d have .2 of the candy bar…is this making sense?

Let’s check: if you are given .3 of a banana you’d have ___________tenths of a banana or ______ pieces out of __________ of the banana.

**Place values are very important for understanding decimals. Here’s help for place values and decimals.**

“.1” is one** tenth **and that is **one space to the right of the “.”**

“.12” is 12 **hundredths** and that means that there’s number** **(2)** two spaces to the right of the “.” **

.101 is one hundred and one **thousandths **and there’s a number** **(1)** three spaces to the right of the “.”**

.2001 is two thousand and one **ten-thousandths, obviously the 1 of 2001 is four places to the right of the “.” **

Here’s a look at decimal place values to the hundred-millionth place:

Let’s try naming the decimal places below:

For the decimal .21634 we have:

_____ in the tenths place
_____ in the hundredths place _____ in the thousandths place _____ in the ten thousandths place _____ in the hundred thousandths place |

Let’s name these decimals:

.02 is 2 _________
.5 is 5 __________ .004 is 4 _________ .00007 is 7 ________ |

Here’s another exercise to check your understanding:

3 hundreths = ________ |

When doing the above problems, remember the last number to the right of the decimal point names the decimal and determines it’s value…

For example, .022 = 22 Thousandths…does that help?

Use the exercise below for more help naming decimal place values.

**Still stumped? Re-read the above information, it’s very important to understand this completely before moving on.**

If you understand fractions, it may help to convert some decimals to fractions. Converting .25 is the same as 25/100 or reduced that’s 1/4

Likewise .33 is the same as 33/100 or reduced it’s about 1/3.

And .75 is the same as 75/100 or reduced that’s 3/4…see the pattern?

(We used 100 as the denominator above since there are two numbers to the right of the “.” in the decimals. We’d use 10 as a denominator if we were converting decimals with only one number to the right of the decimal point or “.” such as .4 or .8 …I hope this is making sense :->))

Decimals are often used with whole numbers. For example, 2.4 (two point four) is read as 2 “and” 4 tenths. What this means in terms of bananas is that you’d have 2 whole bananas and 4 pieces out of ten of another banana.

What this means:

Let’s say we have 3 oranges and 2 pieces out of 10 of another orange. Write the decimal for that here: _______.

Draw a picture of 3.2 oranges below:

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