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Significant Digits and Metric Conversions

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by

Synthia Rey

on 28 August 2013

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Transcript of Significant Digits and Metric Conversions

Significant Digits and Metric Conversions
Synthia Rey 1st pd
Significant Digits
Rules
1.- All non-zero digits are always significant. (1-9)
Ex.- 1.97 has 3 significant digits.

2.- Zeros to the left of other numbers are not significant.
Ex.- 0.042 has 2 significant digits.

3.- Zeros between non-zero digits are always significant.
Ex.- 50.78 has 4 significant digits.

4.- Zeros to the right of the decimal point and at the end of a number are always significant.
Ex.- .200 has 3 significant digits. 30. has 2 significant digits. 30 has 1 significant digit.
Addition and Subtraction
Multiplication and Division
1.- Count the number or decimal places.
2.- Add or subtract normally.
3.- Round the answer to the least number of decimal places that were in the problem.

14.65 + 1.794= 16.444 16.44
629 + 47.68= 676.68 677
15.27-3.847= 11.423 11.42
1.- Look at the problem and count the significant figures in each number.
2.- Solve normally
3.- The answer must be rounded off to have the same number of significant figures as in the component with less significant digits from the problem.
11.74 x 1.9472= 22.860128 22.8601
1000 x 728= 728000 700000
12/3.49= 3.438395415473 3.4
578/1= 578 600
62/41= 1.512195122 1.5
Scientific Notation
143.8 x 10^19 has 4 significant digits

108.0410 x 10^2 has 7 significant digits.
Ignore
this
Scientific Notation and Division
Scientific Notation and Addition
Break the problem into two smaller problems.
Solve
Simplify

(2.113 x 10^4) + (9.2 x 10^4)=
2.113 + 9.2 10^4 + 10^4
11.313 10^4 11.3 x 10^4
(1.13 x 10^5)
Same for subtraction.
When we move the decimal place to the left the exponent on ten increases.
The powers of 10 have to be the same
For multiplication is the same
When we move decimal places to the right, we take the exponent from the ten and we move it one down.
Remember that in scientific notation we need 1 digit to the left of the decimal point.
When we divide numbers we subtract the exponent.
Break the problem into two smaller problems.
Solve and round the significant digits.
Simplify
(2.0 x 10^12) / (8.330 x 10^8)=
2.0 / 8.330 10^12 / 10^8
0.240096 12-8 0.24 x 10^4
(2.4 x 10^3)
Scientific Notation and Significant Zeros
Solve normally and count how many significant digits they have.

Write the answer in scientific notation.

50.00 x 140.0 = 7,000
7.000 x 10^3




112560 / 56.28 = 2,000
2.00 x 10^3
4 4 1
5 4 1
Solve and count the significant digits.
Simplify.
Write in scientific notation.

20.0 x 100.0 = 2,000
2.00 x 10^3

86 x 23 = 1978
2000
2.0 x 10^3

8.9 x 56 = 498.4
500
5.0 x 10^2
3 4 1
2 2 4
2 2 4
Metric Conversions

Ladder Method
King Henry Died Monday Drinking Chocolate Milk

K
H
D
M
L
G
D
C
M
Decrease→
( smaller units)

(bigger units)
←Increase

How to use the ladder method
K
H
D
M
L
G
D
C
M
1.- Determine your starting unit.
2.- Move to your new unit counting the jumps.
3.- Move the decimal the same number of jumps and in the same direction.
6
kg
=
g
6
.0 0 0.
4kg= 6000 g


K
H
D
M
L
G
D
C
M
5.5
cm
=
km


. 0 0 0 0 5.
5
5.5 cm= .000055 km

K
H
D
M
L
G
D
C
M
7500
mL
= _____
L
7
.5 0 0.
7500 mL= 7.5 L




K
H
D
M
L
G
D
C
M
Full transcript