What are decimals?

Intros

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Lessons

What are decimals and how do you read decimals on a number line?
What are decimal place values?
How do we write decimals in standard, expanded, and written forms?
How can we use base ten (block) models to represent decimals?

Examples

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Lessons

Reading decimals on number lines
What are the decimal numbers given by each point shown on the number lines below in:
1. Tenths
2. Hundredths
3. Thousandths
Naming decimal place values
Name the place value that is underlined in the numbers below:
1. 1.83
2. 7.88
3. 9.801
4. 0.845
5. 83.271
Decimal place value word problem
Take a look at the two times the number "5" appears in this number: 5,124,368.057
1. Name the two place values that the two 5s sit inside?
2. 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
1. Rewrite the decimal 0.126 (given in standard form) into
  1. Expanded form and
  2. Written form
2. Rewrite the expanded decimal of (4×0.1) + (5×0.01) + (3×0.001) into standard form.
3. Rewrite the written decimal of seven ones, eight tenths, three hundredths, and nine thousandths into standard form.
Base ten (block) models for hundredths
Using base ten models where one whole is represented by a big square (made of 10 tiny squares), answer the following:
1. What decimal is represented by the picture below?
2. Draw the blocks you would need to show the decimal 6.29
Base ten (block) models for thousandths
Using base ten models where one whole is represented by a cube (made of 1000 tiny squares), answer the following:
1. What decimal is represented by the picture below?
2. Draw the blocks you would need to show the decimal 9.645