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Get Started Now- Intro Lesson: a3:07
- Intro Lesson: b1:38
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- Intro Lesson: d3:53
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- Intro Lesson: f12:10
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- Lesson: 5a2:18
- Lesson: 5b1:41
- Lesson: 5c1:19

In this lesson, we will learn:

- What are equivalent decimal fractions (denominators that are powers of 10)
- How to convert between decimals and decimal fractions
- How to convert between decimals and non-decimal fractions
- How to represent decimal fractions with base ten (block) models

- Decimals are also the
! We talked about decimals as the place values smaller than the**short form of a fraction****ones place**, but they are also another way to write fractions. are fractions with a**Decimal fractions****denominator**that is a power of 10 (Ex. $\frac{5}{10}, \frac{73}{100}, \frac{426}{1000}$)- How do we
__convert__between**decimals**and**decimal fractions**? - To convert a
**decimal**into a**decimal fraction**: - Take
__all the digits of the decimal__and put them in the fraction’s**numerator**as a**whole number**(and remove any**leading zeroes**) - Ex. 0.073= $\frac{73}{?}$
- Look at the
__number of decimal place values__in your decimal, that’s how many zeroes you will put in your fraction’s**denominator** - Ex. 0.0
__7____3__=$\frac{73}{1000}$ - To convert a
**decimal fraction**into a**decimal**: - Look at the
__number zeroes__in the denominator, that’s how many__decimal place values__you will have in your decimal - Ex. $\frac{73}{1000}$ = 0. _ _ _
- Take all the
__numbers in your numerator__; start from the__smallest place values__on the right and fill in the number**backwards (back-fill**them); any empty place values will be filled in with**leading zeroes**. - Ex. $\frac{73}{1000}$ = 0. _ _ _ $\,$→$\,$ 0. _ _
__3__$\,$→$\,$ 0. ___7____3__$\,$→$\,$ 0.__0____7____3__ **Trailing zeroes**are__not__important in the**value**of a decimal number.- Ex. 0.5 and 0.50 are the same! This is because $\frac{5}{10}$ = $\frac{50}{100}$
**Tenths**and**hundredths**are easily converted into**equivalent fractions**(factor of 10). This is also true for**hundredths**and**thousandths**- Ex. 0.50 = 0.500 because $\frac{50}{100}$ = $\frac{500}{1000}$
- What are NOT
**decimal fractions?** - Other fractions with denominators that are NOT
**powers of ten**are(Ex. $\frac{1}{2}$, $\frac{2}{5}$, $\frac{5}{18}$, $\frac{7}{25}$, $\frac{547}{900}$)__non-decimal fractions__ - Some non-decimal fractions have
**denominators**that are**factors**or**multiples**of powers of 10 - They can be converted into
**equivalent**decimal fractions - The common fractions that you should know the decimal values for are:

- To represent decimal fractions with
**base ten (block) models**: - (1) figure out what pieces represents what place value
- (2) tally the number of each tenth, hundredth, thousandth
- (3) and finally, write in standard form and/or fraction form
- We can represent more than one
**whole**for base ten models and decimals. - Fractions that represent greater than one whole are
__mixed fractions__ - Follow the same three steps as before
- The number of
__complete wholes__is written as a big number on the__left side__ - The
__decimal fraction__is written on the__right side__

- IntroductionIntroduction to converting between decimals and fractions:a)What are the different ways to show decimals?b)What are decimal fractions?c)How do we convert between decimal fractions and decimals?d)What are leading and trailing zeroes?e)What are equivalent decimal fractions?f)What are non-decimal fractions and how do we convert them into decimals?g)How do we show decimal fractions using base ten (block) models?
- 1.
**Converting between decimals and decimal fractions**

Recall that decimal fractions are fractions with denominators that are powers of 10 (ex. 10, 100, 1000, etc.).a)Turn each decimal fraction into a decimal:- $\frac{85}{100}$
- $\frac{6}{1000}$
- $\frac{76}{10}$

b)Turn each decimal into a decimal fraction:- .836
- 0.4
- .75

c)Use decimal fractions to write this decimal in expanded form: 1.529 - 2.
**Equivalent tenth and hundredth decimal fractions**

Fill in the chart to understand equivalent tenths and hundredths:a)$\frac{1}{10}$b)$\frac{8}{10}$c)$\frac{10}{10}$ - 3.
**Converting between decimals and non-decimal fractions**

Recall that non-decimal fractions are fractions with denominators that are NOT powers of 10 (i.e. any other numbers besides 10, 100, 1000, etc.)a)Turn each fraction into a decimal:- $\frac{1}{2}$
- $\frac{3}{4}$
- $\frac{4}{5}$
- $\frac{1}{25}$

b)Turn each decimal into a fraction in:__lowest terms__- 0.50
- 2.75
- 1.08
- 3.6

- 4.
**Writing fractions from base ten (block) models**

Write the decimal and fraction represented by the shaded parts of each base ten (block) model:a)b)c)d)e) - 5.
**Decimals and fractions word problem:**

Jimmy and his friends are drinking juice together. After 10 minutes, they measure how much juice they each have left over in their cups and turn those amounts into decimal fractions. Who changed their decimals into fractions correctly?a)Jimmy's glass has 0.2 L of orange juice and he says, "that's a fraction of 0.20 L".b)Noah has 0.68 L of apple juice in his glass and he says, "that's a fraction of $\frac{68}{10}$".c)Ben has 0.075 L of mango juice and he says, "that's a fraction of $\frac{75}{1000}$".

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