Decimals, their place values and how to write it

Decimals are a way of writing numbers that are not whole, using a decimal point (.) to separate the whole part from the fractional part.

🔹 What is a Decimal?

A decimal shows parts of a whole, based on powers of 10.

For example:
3.5 means 3 whole parts and 5 tenths.
0.75 means 75 hundredths.

🔹 Place Values After the Decimal:

Each place after the decimal point has a special name:

0.1 → tenths

0.01 → hundredths

0.001 → thousandths

Decimals help us represent and work with numbers that aren't whole, using powers of 10. They're essential for precise calculations in daily life.

1. PLACE VALUE WITH
DECIMALS
Math 6

2. How do I know what kind of decimal it is?
The name of a decimal is determined by the number
of places to the right of the decimal point
Number of Places Decimal Name Example
1 tenths 0.7
2 hundredths 0.05
3 thousandths 0.016

3. What are mixed decimals?
Mixed decimals are numbers with both whole
numbers and decimals
The name of a whole number is determined by the
number of places to the left of the decimal point
In the number 128.765, 1 is in the hundreds place, 2 is in the
tens place, 8 is in the ones place, 7 is in the tenths place, 6 is
in the hundredths place, and 5 is in the thousandths place

4. How do you read decimals?
To read a decimal correctly, first find the decimal
point
Whole numbers are to the left of the decimal point;
any numbers to the right of a decimal point form a
decimal fraction
Say “and” for the decimal point
The decimal 2164.511 is read as “two thousand, one hundred
sixty-four and five hundred eleven thousandths”

5. Zeros after the decimal point
Writing extra zeros after the decimal point does not
change the value!
The decimals 0.2, 0.20, and 0.200 are equivalent decimals

6. Practice

7. Exercise 1
Write the decimals.
1.Five thousandths
2.Ninety-four thousandths
3.Three hundred thirty-six and sixty-nine hundredths

8. Exercise 2
Write each decimal in words.
1.7884.011
2.5592.4
3.4.203
4.612.250
5.10.44

9. Exercise 3
In what place (on the place value chart) is the
underlined digit? Write the answer.
1.1.475
2.3.763
3.7780.215
4.412.407
5.902.103

10. Exercise 4
Write a decimal that has the same number.
1.0.2
2.5.51
3.410.6
4.753.809

11. Conversions
Decimals to Fractions
and
Fractions to Decimals

12. How to Convert Decimals to Fractions
Use the place value of the last digit in the
number to determine what the
denominator of the fraction will be.

13. How to Convert Decimals to Fractions
.24

14. How to Convert Decimals to Fractions
.5
The 5 is in the
tenths place
10
5

15. How to Convert Decimals to Fractions
.84
The 4 is in the
hundredths place
100
84

16. What if there is a whole number before
the decimal point?
1.589
The 9 is in the
thousandths place
1000
589
1

17. 25.5
The 5 is in the
tenths place
10
5
25
What if there is a whole
number before the decimal
point?

18. How to Convert Fractions to Decimals
100
23
This is the hundredths
place so the 3 needs to
be in the hundredths
place.
2 3
.23

19. How to Convert Fractions to Decimals
1000
567
This is the thousandths
place so the 7 needs to
be in the thousandths
place.
5 6
.567
7

20. How to Convert Fractions to Decimals
1000
4
This is the thousandths
place so the 4 needs to
be in the thousandths
place.
0 0
.004
4

21. How to Convert Fractions to Decimals
10
2
This is the tenths place
so the 2 needs to be in
the tenths place.
2
.2

22. What if there is a whole number before
the fraction?
1000
567
This is the thousandths
place so the 7 needs to
be in the thousandths
place.
5 6
3.567
7
3
3

23. How to Convert Fractions to Decimals
1000
34
24.034
24
This is the thousandths
place so the 4 needs to
be in the thousandths
place.

24. Suppose You Can’t Use A Denominator of 10?
6
5
Divide
the
Numerator
by the
Denominator

25. Suppose You Can’t Use A Denominator of 10?
6
5
65.0
.8
4 8
2
0
0
3
18
2
.83

26. Suppose You Can’t Use A Denominator of 10?
3
2
32.0
.6
1 8
2
.6

28. Try Some . . .
8
7
50
5
10
6
4
3
16
12
40
3

29. Try Some . . .
.35.25.95
.6.875.125

30. Comparing Decimals
How do we compare decimals?
When we compare we use terms such as:
Less than <
Greater than >
Equal to =
Comparing decimals is similar to comparing
whole numbers.
45<47
150>105
When we compare decimals we use place
value or a number line.

31. Example:
Compare Sara’s score with
Danny’s score.
1.Line Up Decimal Points
Sara: 42.1
Danny: 42.5
2.Start at the left and find the first place
where the digits differ. Compare the
digits
1<5
42.1<42.5
This means Sara’s score was lower
than Danny’s score.
SaraSara 42.142.1
DannyDanny42.542.5
RossRoss 42.042.0
BethanBethan
yy
40.740.7
JacobJacob46.146.1
Half pipe Results

32. Let’s Try Using A Number Line
SaraSara 42.142.1
DannyDanny 42.542.5
RossRoss 42.042.0
BethanyBethany40.740.7
JacobJacob 46.146.1
42.042.1 42.5
Numbers to the right are
greater than numbers to
the left. Since 42.5 is to the
right of 42.1 we have:
42.5>42.1

33. Equivalent Decimals
Decimals that name the same number are
called equivalent decimals.
0.60 and 0.6
Are these the same???

34. 0.60 0.6=

35. Adding Zeros
This means placing a zero to the right of
the last digit in a decimal.
0.6 0.60
Although we added a zero, the value of the
decimal did not change!!
Adding zeros is useful when ordering a
group of decimals.

36. Ordering Decimals
We can order decimals from least to
greatest or we can order from greatest to
least.
Let’s try this example:
Order 15, 14.95, 15.8, and 15.01 from least
to greatest

37. First, line up the decimal points
15
14.95
15.8
15.01
15, 14.95, 15.8, 15.01

38. 15, 14.95, 15.8, 15.01
Next, add zeros so that each
number has the same number of
decimal places
15.00
14.95
15.80
15.01

39. Finally, use place value to compare the
decimals. Always start from the left.
15.00
14.95
15.80
15.01
14.95, 15, 15.01, 15.8
15, 14.95, 15.8, 15.01

40. Order these numbers from
greatest to least
35.06, 35.7, 35.5, 35.84

41. Exercises

45. Exercises

48. Exercises

49. Dividing Decimals with Whole Number
Dividing decimals by whole numbers is
similar to normal division. Here, the dividend
is a decimal number and the divisor is a
whole number, so the decimal point in the
quotient will be placed according to the
decimal point of the dividend. We can
understand this with the help of the long
division of decimals.
Example: Divide 338.56 ÷ 23

50. Dividing Decimals with Whole
Number
Step 1: First, write the
 division in the
standard form. Start by dividing the
whole number part by the divisor.
Step 2: Place the decimal point in the
quotient above the decimal point of the
dividend. Bring down the tenth digit.
Step 3: Divide and bring down the other
digit in sequence. Divide until 0 is
obtained in the
 remainder. Thus, the
decimal in the quotient is placed
according to the decimal in the dividend.

51. Exercises

52. Dividing Decimals with Decimals
For dividing decimals by another decimal,
we need to convert the divisor into a whole
number and then continue the division. Let
us understand the conditions and rules for
this method using an example.
Example: Divide 48.65 ÷ 3.5

53. Step 1: The dividend is 48.65 and the
divisor is 3.5. We need to change the divisor
to a whole number and so we will multiply it
by 10 so that the decimal point shifts to the
right and it becomes a whole number. This
means, 3.5 × 10 = 35.
Step 2: We need to treat the dividend in the
same way as we had treated the divisor. So,
we will multiply the dividend by 10 as well.
This means it will be 48.65 × 10 = 486.5. In
other words, we need to move both the
decimal points to the right until the divisor
becomes a whole number.
Step 3: Now, we have 486.5 as the dividend
and 35 as the divisor. This can be divided as
we do the usual division and we get 13.9 as
the quotient.

54. Exercises

55. Important Tips on Dividing Decimals
•Convert the divisor to a whole number by
multiplying by the powers of 10. Multiply the
dividend by the same powers of 10.
•In order to divide a decimal number by 10, move
the decimal point to the left by one place. For
example, if we need to divide 45.67 ÷ 10, then it
can be easily done by shifting the decimal point
to the left and the answer will be 4.567

56. Important Tips on Dividing Decimals
•In order to divide a decimal number by 100, move
the decimal point to the left by two places. For
example, if we need to divide 324.6 ÷ 100, then it
can be easily done by shifting the decimal point
to the left and the answer will be 3.246
•In order to divide a decimal number by 1000,
move the decimal point to the left by three places.
For example, if we need to divide 8934.5 ÷ 1000,
then it can be easily done by shifting the decimal
point to the left and the answer will be 8.9345