Topic B: Decimal fractions and place value patterns

##Expanded form

Expanded form is a way to write numbers by adding the value of its digits.

We can use a place value chart to think of the value of a number's digit.

###Example

Let's write $\blueD3.\purpleD4\greenD0\maroonD5$ in expanded form.

$3.405=\blueD{3}\text{ ones}$ $+,\purpleD{4}\text{ tenths}+$ $\greenD{0}\text{ hundredths}+\maroonD5\text{ thousandths}$

$\phantom{3.405}=(\blueD{3}\times1)+\left(\purpleD{4}\times\dfrac1{10}\right)$$+\left(\greenD{0}\times\dfrac1{100}\right)+\left(\maroonD{5}\times\dfrac1{1000}\right)$

$\phantom{3.405}=\blueD{3}+\purpleD{\dfrac4{10}}+\greenD{0}+\maroonD{\dfrac5{1000}}$

$3.405$ in expanded form is $\blueD{3}+\purpleD{\dfrac4{10}}+\maroonD{\dfrac5{1000}}$.

[[☃ explanation 1]]

Want to learn more about expanded form? Check out this video.

##Practice

[[☃ graded-group-set 2]]

Want to try more problems like this? Check out this exercise.

##Written form

Written form is a way to write numbers using only words.

###Example

Let's write $\blueD3.\purpleD40\maroonD5$ in written form.

$3.405=\blueD{3}\text{ ones}+,\purpleD{4}{0}\maroonD5\text{ thousandths}$

First, we will read the number to the left of the decimal.

$\blueD{\text{Three}}$

Then, we read the decimal as "$\text{\goldD{and}}$".

$\blueD{\text{Three}} \goldD{\text{ and}}$

Finally, we read the numbers to the right of the decimal and state the place value of the digit farthest to the right.

$\blueD{\text{Three}}\goldD{\text{ and}} $ $\text{ \purpleD{four} hundred \maroonD{five} thousandths} $

$3.405$ in written form is three and four hundred five thousandths.

Want to learn more about written form? Check out this video.

##Practice

[[☃ graded-group-set 1]]

Want to try more problems like this? Check out this exercise.