# What are decimals?

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##### Intros

###### Lessons

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##### Examples

###### Lessons

**Reading decimals on number lines**

What are the decimal numbers given by each point shown on the number lines below in:**Naming decimal place values**

Name the place value that is underlined in the numbers below:- 1.
__8__3 - 7.8
__8__ - 9.80
__1__ __0__.845__8__3.271

- 1.
**Decimal place value word problem**

Take a look at the two times the number "5" appears in this number:__5__,124,368.0__5__7- Name the two place values that the two 5s sit inside?
- Compare these two place values; how many times do you have to multiply/divide by 10 to get to the other place value? How many times will you have to group ten into a bigger place value (or the other way, split into ten parts for a smaller place value) to get to the other place value?

**Converting decimals between standard, expanded, and written forms****Base ten (block) models for hundredths**

Using base ten models where one whole is represented by a(made of 10 tiny squares), answer the following:__big square__**Base ten (block) models for thousandths**

Using base ten models where one whole is represented by a(made of 1000 tiny squares), answer the following:__cube__

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###### Topic Notes

In this lesson, we will learn:

- How to understand decimals using number lines
- How to understand decimals using place values
- How to represent decimals using standard form, expanded form, and written forms
- How to use base ten (block) models to represent decimals

__Notes:__- When we look at a number that has
**multiple digits**, each**place value**is 10 times__MORE__than the place on its right, and 10 times__LESS__than the place on its left. - For example, when we look at the
, we start counting until 10 which starts the__ones__place value:__tens__place value - Then, we group ten 10s to get to the next
**place value**of:__hundreds__ - Continuing, we can then group ten 100s to get to the
and ten 1000s to get to the__thousands__place value…etc.__ten-thousands__place value - The same rule applies for decimals!
**Decimals**are**place values**that are__even smaller__than the(to the right of the__ones__place**decimal point**), and the numbers (**place values**) are further split into ten parts (divisions). - This can be shown on a number line, splitting into
:__tenths__

- If we split the number line even further, each
can be divided into__tenth__and__hundredths__:__thousandths__

**place values**for

**decimals**

__mirror__the names of the

**whole number place values**, but you need to add the “

*-ths*” suffix to the end.

**standard form, expanded form**, or even

**written from**:

**Standard form**shows all the numbers written from left to right, with a decimal point after the ones place- Ex. 165.407
**Expanded form**shows the value of the digit multiplied by how much each place value represents.- Ex. (1×100) + (6×10) + (5×1) + (4×0.1) +
~~(0×0.01)~~+ (7×0.001) **Place values**that hold a zero can be left out of**expanded form****Written form**shows how to write out decimals as__words__! Name the number of each digit followed by the name of the place value:- Ex. one hundred sixty-five and four tenths,
~~zero hundredths~~, and seven thousandths

**base ten models (place value blocks)**to show decimals too—not only whole numbers

- Our whole numbers will always refer to the
place value (or greater)__ones__ - If our number only represents until the
place, then one whole is__hundredths__**one-hundred block**:

**place, then**

__thousandths__**one whole is one-thousand block**:

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