Decimals


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 = ________
41 thousandths = ________
8 tenths = _________
22 ten thousandths = _________

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:

 

Page 2 of Decimals