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- Decimals

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Try reviewing these fundamentals first

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Get Started Now- Intro Lesson: a14:09
- Intro Lesson: b4:02
- Intro Lesson: c4:49
- Intro Lesson: d4:10
- Lesson: 1a4:34
- Lesson: 1b7:18
- Lesson: 1c5:33
- Lesson: 24:27
- Lesson: 3a2:49
- Lesson: 3b2:04
- Lesson: 4a4:32
- Lesson: 4b1:40
- Lesson: 4c1:05
- Lesson: 5a2:15
- Lesson: 5b1:21
- Lesson: 6a3:24
- Lesson: 6b2:03

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

- 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__

**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

- 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**:

- IntroductionIntroduction to decimals:a)What are decimals and how do you read decimals on a number line?b)What are decimal place values?c)How do we write decimals in standard, expanded, and written forms?d)How can we use base ten (block) models to represent decimals?
- 1.
**Reading decimals on number lines**

What are the decimal numbers given by each point shown on the number lines below in:a)Tenths

b)Hundredthsc)Thousandths - 2.
**Naming decimal place values**

Name the place value that is underlined in the numbers below:a)1.__8__3b)7.8__8__c)9.80__1__d)__0__.845e)__8__3.271 - 3.
**Decimal place value word problem**

Take a look at the two times the number "5" appears in this number:__5__,124,368.0__5__7a)Name the two place values that the two 5s sit inside?b)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? - 4.
**Converting decimals between standard, expanded, and written forms**a)Rewrite the decimal 0.126 (given in standard form) into- Expanded form and
- Written form

b)Rewrite the expanded decimal of (4×0.1) + (5×0.01) + (3×0.001) into standard form.c)Rewrite the written decimal of seven ones, eight tenths, three hundredths, and nine thousandths into standard form. - 5.
**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__a)What decimal is represented by the picture below?b)Draw the blocks you would need to show the decimal 6.29 - 6.
**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__a)What decimal is represented by the picture below?b)Draw the blocks you would need to show the decimal 9.645

10.

Decimals

10.1

What are decimals?

10.2

Multiplying decimals by powers of 10

10.3

Dividing decimals by powers of 10

10.4

Coverting between decimals and fractions

10.5

Comparing and ordering decimals and fractions

10.6

Multiplying decimals with integers

10.7

Dividing decimals with integers

10.8

Word problems for decimals and integers