THE METRIC SYSTEM

WHY DO WE USE THE METRIC SYSTEM?

Almost all other countries are using the metric system

Scientists need a universal way to communicate data (SI Units)

THE METRIC CONVERSION CHART (STAIRCASE METHOD)

Kilo1000units

Hecto100units

Deka10

unitsBasic Unit Deci

0.1units

Centi0.01units

Milli0.001units

To convert to a smaller unit, movedecimal point to the right or

multiply.

To convert to a larger unit, movedecimal point to the left or divide

YouTube - metric conversions - shortcut method

Do the following conversions… 1678 mg to kg’s _____________ 456 liters to ml’s ____________ 6,789,000 mm’s to km’s

_____________ 1 liter to dl’s _____________ 45 cm’s to km’s _______________

TRY THIS USING THE STAIRCASE METHOD

1000 mg = ______ g

Step 1: Determine if you are going to go up or down the ladder.Step 2: Determine how many steps there are from milligrams to grams.Step 3: Move the decimal point the amount of places that was determined in steps 1 & 2.

TRY THIS USING THE STAIRCASE METHOD

1000 mg = ______ g

Step 1: Determine if you are going to go up or down the ladder.Step 2: Determine how many steps there are from milligrams to grams.Step 3: Move the decimal point the amount of places that was determined in steps 1 & 2.

1

TRY THIS USING THE STAIRCASE METHOD

.15 L = __________ ml

TRY THIS USING THE STAIRCASE METHOD

.15 L = __________ ml150

Scientific Notation

A short-hand way of writinglarge numbers without writing all of the zeros.

The Distance From the Sun to the Earth

93,000,000

Step 1

Move decimal left Leave only one number in front of

decimal

Step 2

Write number without zeros

Step 3

Count how many places you moved decimal

Make that your power of ten

The power often is 7 becausethe decimalmoved 7 places.

93,000,000 --- Standard Form

9.3 x 107 --- Scientific Notation

Practice Problem

1) 98,500,000 = 9.85 x 10?

2) 64,100,000,000 = 6.41 x 10?

3) 279,000,000 = 2.79 x 10?

4) 4,200,000 = 4.2 x 10?

Write in scientific notation. Decide the power of ten.

9.85 x 107

6.41 x 1010

2.79 x 108

4.2 x 106

More Practice Problems

1) 734,000,000 = ______ x 108

2) 870,000,000,000 = ______x 1011

3) 90,000,000,000 = _____ x 1010

On these, decide where the decimal will be moved.

1) 7.34 x 108 2) 8.7 x 1011 3) 9 x 1010

Complete Practice Problems

1) 50,0002) 7,200,0003) 802,000,000,000

Write in scientific notation.

1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

Scientific Notation to Standard Form

Move the decimal to the right

3.4 x 105 in scientific notation

340,000 in standard form

3.40000 --- move the decimal

Write in Standard Form

6.27 x 106

9.01 x 104

6,270,000 90,100

Significant Figures

1.8

• Any digit that is not zero is significant

1.234 kg 4 significant figures• Zeros between nonzero digits are significant

606 m 3 significant figures• Zeros to the left of the first nonzero digit are not significant

0.08 L 1 significant figure• If a number is greater than 1, then all zeros to the right of the

decimal point are significant

2.0 mg 2 significant figures• If a number is less than 1, then only the zeros that are at the

end and in the middle of the number are significant

0.00420 g 3 significant figures

How many significant figures are in each of the following measurements?

24 mL 2 significant figures

3001 g 4 significant figures

0.0320 m3 3 significant figures

6.4 x 104 molecules 2 significant figures

560 kg 2 significant figures

1.8

Significant Figures

1.8

Addition or Subtraction

The answer cannot have more digits to the right of the decimalpoint than any of the original numbers.

89.3321.1+

90.432 round off to 90.4

one significant figure after decimal point

3.70-2.91330.7867

two significant figures after decimal point

round off to 0.79

If you round off to a “5”, if the next digit is ODD, round up. If it is EVEN, round down (leave it)!

Significant Figures

1.8

Multiplication or Division

The number of significant figures in the result is set by the original number that has the smallest number of significant figures

4.51 x 3.6666 = 16.536366 = 16.5

3 sig figs round to3 sig figs

6.8 ÷ 112.04 = 0.0606926

2 sig figs round to2 sig figs

= 0.061

Significant Figures

1.8

Multiplication or Division

The number of significant figures in the result is set by the original number that has the smallest number of significant figures

4.51 x 3.6666 = 16.536366 = 16.5

3 sig figs round to3 sig figs

6.8 ÷ 112.04 = 0.0606926

2 sig figs round to2 sig figs

= 0.061

Accuracy – how close a measurement is to the true value

Precision – how close a set of measurements are to each other

accurate&precise

precisebutnot accurate

not accurate&not precise

1.8

1.9

Dimensional Analysis Method of Solving Problems

1. Determine which unit conversion factor(s) are needed

2. Carry units through calculation

3. If all units cancel except for the desired unit(s), then the problem was solved correctly.

1 L = 1000 mL

How many mL are in 1.63 L?

1L

1000 mL1.63 L x = 1630 mL

1L1000 mL

1.63 L x = 0.001630L2

mL

The speed of sound in air is about 343 m/s. What is this speed in miles per hour?

1 mi = 1609 m 1 min = 60 s 1 hour = 60 min

343ms

x1 mi

1609 m

60 s

1 minx

60 min

1 hourx = 767

mihour

meters to miles

seconds to hours

1.9