Transcript Are the values the same?

hundred-thousandths
ten-thousandths
thousandths
hundredths
tenths
ones
tens
hundreds
thousands
ten-thousands
hundred-thousands
millions
5.1 – Introduction to Decimals
Decimal Notation and Writing Decimals.
2, 4 5 7, 8 3 2 . 8 3 0 9 4
– Introduction
Decimals
4. –5.1
Solving
Equationstowith
Fractions
Decimal Notation and Writing Decimals.
Write each number in words.
0.06
-200.073
0.0829
87.31
52.1085
1493.62
Six hundredths
Negative two hundred and seventy-three
thousandths
Eight hundred twenty-nine ten-thousandths
Eighty-seven and thirty-one hundredths
Fifty-two and one thousand eighty-five tenthousandths
One thousand four hundred ninety-three and
sixty-two hundredths
– Introduction
Decimals
4. –5.1
Solving
Equationstowith
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 twentyfive ten-thousandths
Twelve thousand thirty-seven and two
hundred ninety-eight thousandths
-807.0025
12,037.298
5.1 – Introduction to Decimals
Decimal Notation and Writing Decimals.
Write the following decimals as fractions/mixed numbers in
simplest form.
51
241
0.51
0.241
100
1000
0.032
64.8
32
4
1000
125
8
64
10
4
64
5
29.97
-209.986
97
29
100
986
 209
1000
493
 209
500
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 > 0.00065
3.4251 > 3.4249
-0.562 > -0.652
-0.039
< -0.0309
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.
482.7817 Round to the nearest thousandth
482.782
0.7522
Round to the nearest tenth
3.141592 Round to the nearest hundredth
0.8
3.14
750
752.883
Round to the nearest tens
5.2 – Adding and Subtracting Decimals
Are the values the same?
0.03
0.0003
0.00300
0.3
NO
0.003
0.003
0.003
0.003
0.0030000
0.003000
0.0030
0.00300
YES
YES
Zeros placed at the end of the last digit in a decimal do not
change the value of the decimal.
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 + 5.371
40.08 + 17.612
19.52 0
+ 5.371
40.08 0
+ 17.612
24.891
57.692
5.2 – Adding and Subtracting Decimals
Examples:
0.125 + 422.8
19 + 26.47
0.125
+ 422.800
19 .00
+ 26.47
422.925
45.47
34.567 + 129.43 + 2.8903
34.5670
129.4300
+
2.8903
16 6 .8873
11.21 + 46.013 + 362.526
11.21 0
46.013
+ 362.526
419 .74 9
5.2 – Adding and Subtracting Decimals
Examples:
6.7 – 3.92
73 – 29.31
6.7 0
- 3.92
2 .7 8
73 .00
- 29.31
4 3 .6 9
-5.4 – 9.6
-5.4
-9.6
- 15. 0
7.12 + (-9.92)
-9.92
7.12
- 2.80
5.2 – Adding and Subtracting Decimals
Examples:
19.204 from 25.91
25.91 0
- 19.204
6. 706
Evaluate y – z if y = 11.6 and z = 10.87
11.6 0
- 10.87
0.73
5.2 – Adding and Subtracting Decimals
Examples:
Is 12.14 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 0
7 .84 = 7.84
12.14 is a solution.
5.2 – Adding and Subtracting Decimals
Examples:
-4.3y + 7.8 – 20.18y + 14.602
-4.30y
-20.18y
- 2 4.48 y
7.8 00
14.602
2 2 .4 02
-24.48y + 22.402
5.2 – Adding and Subtracting Decimals
Estimation – a process to check if an answer is reasonable.
Actual (Exact)
58.1 + 326.97
58.1 0
+ 326.97
3 8 5.07
Actual (Exact)
Estimate
60 + 330
60
330
390
Estimate
16.08 – 0.921
16 – 1
16.08 0
- 0.921
1 5 .159
16
- 1
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
x 0.62
696
2088
0.0641
x
27
4487
1282
21576
17307
3 decimal places
21.576
4 decimal places
1.7307
5.3 – Multiplying Decimals
Examples:
7.3
x -0.9
657
2 decimal places
6.57
-0.9
x 7.3
27
63
657
2 decimal places
6.57
5.3 – Multiplying Decimals
Estimate
Actual (Exact)
30.26
x 2.89
27234
24208
6052
874514
4 decimal places
87.4514
30
x 3
90
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.
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
5.3 – Circumference of a Circle
r
d
Blue line = Diameter
Red line = Radius
d = 2r
Circumference – the length around the edge of a circle.
C=d
or
C=2r
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
5.3 – Circumference of a Circle
C=d
C=2r
or
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
x 2
628
2 decimal places
6.28
6.28
x 2.5
3140
1256
15700
3 decimal places
15.700
15.7 feet