7-1 Introduction to Decimals

Transcription

1 7-1 Introduction to Decimals

2 Place Value

3 Place Value

4 Place Value tens

5 Place Value units tens

6 Place Value decimal point units tens

7 Place Value tenths decimal point units tens

8 Place Value hundredths tenths decimal point units tens

9 Place Value thousandths hundredths tenths decimal point units tens

10 Place Value tens units decimal point tenths hundredths thousandths ten-thousandths

11 Place Value tens units decimal point tenths hundredths thousandths ten-thousandths hundred-thousandths

12 Place Value millionths hundred-thousandths ten-thousandths thousandths hundredths tenths decimal point units tens

13 Numbers in Words How can we say the number.401?

14 Numbers in Words How can we say the number.401? four hundred one thousandths

15 Numbers in Words How can we say the number.401? four hundred one thousandths How do we write the number two-hundred thirty-seven ten-thousandths?

16 Numbers in Words How can we say the number.401? four hundred one thousandths How do we write the number two-hundred thirty-seven ten-thousandths?.0237

17 Expanded Form When working with children, we want to represent these decimal numbers as many ways as we can. One way is using expanded form. What is expanded form?

18 Expanded Form When working with children, we want to represent these decimal numbers as many ways as we can. One way is using expanded form. What is expanded form? Write.324 in expanded form.

19 Expanded Form When working with children, we want to represent these decimal numbers as many ways as we can. One way is using expanded form. What is expanded form? Write.324 in expanded form..324 =

20 Expanded Form When working with children, we want to represent these decimal numbers as many ways as we can. One way is using expanded form. What is expanded form? Write.324 in expanded form. Write.0201 in expanded form..324 =

21 Expanded Form When working with children, we want to represent these decimal numbers as many ways as we can. One way is using expanded form. What is expanded form? Write.324 in expanded form. Write.0201 in expanded form..324 = =

22 Expanded Fraction Form Write using fraction expanded form.

23 Expanded Fraction Form Write using fraction expanded form = 1(10) + 3(1)

24 Visually Representing Decimals We have a couple of different ways we can represent decimals.

25 Visually Representing Decimals We have a couple of different ways we can represent decimals. 1 the number line

26 Visually Representing Decimals We have a couple of different ways we can represent decimals. 1 the number line 2 grids

27 Decimals on the Number Line

28 Decimals on the Number Line

29 Decimals on the Number Line

30 Decimals on the Number Line

31 Tenths Grid

32 Tenths Grid

33 Tenths Grid

34 Decimal Squares

35 Decimal Squares

36 Decimal Squares

37 Converting Convert.31 to a fraction in simplest form.

38 Converting Convert.31 to a fraction in simplest form. Convert.051 to a fraction in simplest form.

39 Converting Convert.31 to a fraction in simplest form. Convert.051 to a fraction in simplest form. Convert.0204 to a fraction in simplest form.

40 Converting Convert to a decimal.

41 Converting Convert to a decimal. 201 Convert to a decimal.

42 Converting Convert 3 8 to a decimal.

43 Converting Convert 3 8 to a decimal. Since we don t have a denominator that is a power of 10, we need to get there somehow. Suggestions?

44 Converting Convert 3 8 to a decimal. Since we don t have a denominator that is a power of 10, we need to get there somehow. Suggestions? 3 8

45 Converting Convert 3 8 to a decimal. Since we don t have a denominator that is a power of 10, we need to get there somehow. Suggestions? 3 8 = 3 2 3

46 Converting Convert 3 8 to a decimal. Since we don t have a denominator that is a power of 10, we need to get there somehow. Suggestions? 3 8 = =

47 Converting Convert 3 8 to a decimal. Since we don t have a denominator that is a power of 10, we need to get there somehow. Suggestions? 3 8 = = =

48 Converting Convert 3 8 to a decimal. Since we don t have a denominator that is a power of 10, we need to get there somehow. Suggestions? 3 8 = = = =

49 Converting Convert 3 8 to a decimal. Since we don t have a denominator that is a power of 10, we need to get there somehow. Suggestions? 3 8 = = = = =.375

50 Terminating Decimals The question is, when can we writing a given rational number as a terminating decimal?

51 Terminating Decimals The question is, when can we writing a given rational number as a terminating decimal? Definition A terminating decimal can be written with a finite number of non-zero places to the right of the decimal point.

52 Terminating Decimals The question is, when can we writing a given rational number as a terminating decimal? Definition A terminating decimal can be written with a finite number of non-zero places to the right of the decimal point. Which of the following can be written as terminating decimal?

53 Terminating Decimals Definition A rational number a b, with gcf(a, b) = 1, can be written as a terminating decimal if and only if the prime factorization of the denominator contains only powers of 2 and 5.

54 Ordering Decimals Which is larger?.29 or.3?

55 Ordering Decimals Which is larger?.29 or.3?.003 or.00093?

56 Ordering Decimals Which is larger?.29 or.3?.003 or.00093?.001 or ?

57 Ordering Decimals Which is larger?.29 or.3?.003 or.00093?.001 or ? Can we come up with a rule as to how to decide which is larger when given two terminating decimals?