1. 5.1 – Introduction to Decimals
Decimal Notation and Writing Decimals.
2, ,
tens
ones
millions
tenths
hundreds
thousands
hundredths
thousandths
ten-thousands
ten-thousandths
hundred-thousands
hundred-thousandths

2. 5.1 – Introduction to Decimals 4. – Solving Equations with Fractions
Decimal Notation and Writing Decimals.
Write each number in words.
0.06
Six hundredths
Negative two hundred and seventy-three thousandths
0.0829
Eight hundred twenty-nine ten-thousandths
87.31
Eighty-seven and thirty-one hundredths
Fifty-two and one thousand eighty-five ten-thousandths
One thousand four hundred ninety-three and sixty-two hundredths

3. 5.1 – Introduction to Decimals 4. – Solving Equations with Fractions
Decimal Notation and Writing Decimals.
Write each decimal in standard form.
Five hundred and ninety-six hundredths
500.96
Thirty-nine and forty-two thousandths
39.042
Negative eight hundred seven and twenty-five ten-thousandths
Twelve thousand thirty-seven and two hundred ninety-eight thousandths
12,

4. 5.1 – Introduction to Decimals
Decimal Notation and Writing Decimals.
Write the following decimals as fractions/mixed numbers in simplest form.
0.51
0.241
0.032
29.97
64.8

5. 5.1 – Introduction to Decimals
Comparing Decimals
Compare digits in the same place, when determining which number is larger.
When two digits are not the same value, the larger digit is the larger decimal.
Use < or > to make a true statement
26.208
<
26.28
0.12
>
0.026
0.0065
>
3.4251
>
3.4249
-0.562
>
-0.652
-0.039
<

6. 5.1 – Introduction to Decimals
Rounding Decimals
Locate the digit to the right of the requested place value.
If the digit to the right is 5 or greater, round the place value up one and drop remaining digits.
If the digit to the right is less than 5, the place value remains and the remaining digits are dropped.
Round to the nearest thousandth
0.7522
Round to the nearest tenth
0.8
Round to the nearest hundredth
3.14
Round to the nearest tens
750

7. 5.2 – Adding and Subtracting Decimals
Are the values the same?
0.03
0.003
0.0003
0.003
0.003
0.0030
0.3
0.003 NO
YES
YES
Zeros placed at the end of the last digit in a decimal do not change the value of the decimal.

8. 5.2 – Adding and Subtracting Decimals
1) Write the numbers so the decimal points line up vertically.
2) Place zeros after the last digit to assist in adding or subtracting the decimals.
3) Add or subtract the decimal places like whole numbers.
Examples:
19.52
40.08 +
5.371 +
17.612
24.891
57.692

9. 5.2 – Adding and Subtracting Decimals
Examples:
0.125 19
.00 +
422.8 00 +
26.47
45.47
34.567
11.21
129.43 00
46.013 +
2.8903 + 1 6 6 . 8 8 7 3 4 1 9 . 7 4 9

10. 5.2 – Adding and Subtracting Decimals
Examples:
6.7 – 3.92
73 – 29.31
6.7 73
.00 -
3.92 -
29.31 2 . 7 8 4 3 . 6 9
-5.4 – 9.6
(-9.92)
-5.4
-9.92
-9.6
7.12 - 15 . - 2 . 8

11. 5.2 – Adding and Subtracting Decimals
Examples:
from 25.91
25.91 -
19.204 6 . 7 6
Evaluate y – z if y = 11.6 and z = 10.87
11.6 -
10.87 . 7 3

12. 5.2 – Adding and Subtracting Decimals
Examples:
Is a solution of the equation y – 4.3 = 7.84?
y – 4.3 = 7.84
12.14 – 4.3 = 7.84
12.14 -
4.3 7 . 8 4 =
7.84
12.14 is a solution.

13. 5.2 – Adding and Subtracting Decimals
Examples:
-4.3y – 20.18y
-4.30y
7.8 00
-20.18y
14.602 - 2 4 . 4 8 y 2 2 . 4 2
-24.48y

14. 5.2 – Adding and Subtracting Decimals
Estimation – a process to check if an answer is reasonable.
Actual (Exact)
Estimate
58.1 60 +
326.97
330 3 8 5 . 7
390
Actual (Exact)
Estimate
16.08 – 0.921
16 – 1
16.08 16 -
0.921 - 1 1 5 . 1 5 9 15

15. 5.3 – Multiplying Decimals
1) Multiply the decimals as thought they are whole numbers.
2) Add the number of decimal places in each term.
3) From the last digit of the product, count to the left and place the decimal after that numbered term.
Examples:
34.8
0.0641 x
0.62 x 27
696
4487
2088
1282
21576
17307
3 decimal places
4 decimal places
21.576
1.7307

16. 5.3 – Multiplying Decimals
Examples:
7.3
-0.9 x
-0.9 x
7.3
657 27 63
2 decimal places
657
6.57
2 decimal places
6.57

17. 5.3 – Multiplying Decimals
Actual (Exact)
Estimate
30.26 30 x
2.89 x 3
27234 90
24208
6052
874514
4 decimal places

18. 5.3 – Multiplying Decimals
Examples:
Is -5.5 a solution of the equation: – 6x = 33?
-6 (-5.5)
5.5 x 6
330
1 decimal place
33.0 = 33
-5.5 is a solution.

19. 5.3 – Multiplying Decimals
A garden contains 60.5 square yards of space for planting. The fertilizer to be used on the garden suggests a spreading rate of 5.6 ounces per square yard. How many ounces of fertilizer are needed?
60.5 x
5.6
3630
3025
33880
2 decimal places
338.80
338.8
ounces

20. 5.3 – Circumference of a Circle
Blue line = Diameter r
Red line = Radius d
d = 2r
Circumference – the length around the edge of a circle.
C =  d or
C = 2  r

21. 5.3 – Circumference of a Circle
C =  d or
C = 2  r
Find the circumference of a circle whose diameter is 7 meters.
( Use 3.14 as an approximation of .)
C = 3.14 (7)
3.14 x 7
2198
2 decimal places
21.98
meters

22. 5.3 – Circumference of a Circle
C =  d or
C = 2  r
Find the circumference of a circle whose radius is 2.5 feet.
( Use 3.14 as an approximation of .)
C =2 (3.14) (2.5)
3.14
6.28 x 2 x
2.5
628
3140
2 decimal places
1256
15700
6.28
3 decimal places
15.700
15.7
feet