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Metric Conversions Ladder Method

T. Trimpe 2008 http://sciencespot.net/

+Countries That Do Not Use the Metric System

Liberia

Burma/Myanmar

U.S.

+The Magic of the Metric System:

10x!

meter(m)gram(g)liter(L)

kkilo-1000x

ccenti-0.01x m

milli-0.001x

Distance/length

Mass

Volume

BASE UNIT

Big -> Small

‘CKats’ hate dogs because dogs can’t meow

100x

10x

1/10x0.1x

smaller

bigger

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1.0

kilo-

milli-

1. You have 0.33 kilograms of laundry soap; how many grams?

2. Your water bottle is labeled 500mL; how many liters does it hold?

0.3 3

0g

# of stair steps = # of decimal places

5 0 0. L

+How many millimeters in 1 centimeter?

Measuring Length (m)

How long is the line in cm? in mm?

cm

Measuring Mass (g)Please be careful with the scales!

Use ‘tare’ or zero button to ignore the mass of the container

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• Geometric solids use m3

l x w x h

Measuring Volume

• Irregular solids use water displacementVolume of object

• Liquids, use L

mL of a rock!?1mL =1cm3 = 1cc

At eye level, read at the bottom of the meniscus

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What is the volume of water in the cylinder?

What is the volume of the toy?

Recall: 1mL = 1 cm3 (1cc)

Measuring Volume

+Convert one value, using the ladder method, then compare

1) 200cg to g 6) 5 L to mL 11) 16 cm to mm

2) 104 km to m 7) 198 g to kg 12) 2500 m to km

3) 480 cm to m 8) 75 mL to L 13) 65 g to mg

4) 5.6 kg to g 9) 50 cm to m 14) 6.3 cm to mm

Compare using <, >, or =.

25) 63 cm 6 m 27) 5 g 508 mg 29) 1,500 mL 1.5 L

26) 536 cm 53.6 dm 28) 43 mg 5 g 30) 3.6 m 36 cm

Practice

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Wait! I measure distance in

MILES!

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Which is longer?

A. 1 mile or 1 kilometer

B. 1 yard or 1 meter

C. 1 inch or 1 centimeter

1.6 kilometers

1 mile

1 yard = 0.9444 meters

1 inch = 2.54 centimeters

U.S. vs. Metric : Length

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Which is larger?

1. 1 Pound or 100 Grams

2. 1 Kilogram or 1 Pound

3. 1 Ounce or 1000 Milligrams

100 kg = 220 pounds

1 ounce of gold = 28.35 g

U.S. v. Metric: Mass

1 pound = 453.6

g

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Which is larger?

A. 1 liter or 1 gallon

B. 1 liter or 1 quart

C. 1 milliliter or 1 fluid ounce

1 gallon = 3.79L

1 fl oz = 29.53mL1 12-oz can of soda ~ 355 mL

1 quart = 0.946 liters

U.S. v. Metric: Volume

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Dimensional analysisConverting One Unit to Another

Determine these three facts:

Your friend runs a 2.5mi route while you typically run a 5km one.

Which of you ran the longer distance?

• What unit do you need to convert to?

• What conversions factor(s) can be used to ‘bridge’ the two?

• What value & units are you given to convert?

1mi =1.6km

2.5mi 1.6km ------- x -------- 1 1 mi

= 4km you rule!

+ Use a conversion factor with the same units in the denominator as the given units

Multiply across; divide final fraction

Set up answer units in the numerator of one fraction

Cancel like terms (units)

2.5mi 1.6km ------- x -------- 1 1 mi 2.5 (3.2km)

---------- = finish it! 1 (2)

Conversion factor

Go Hog Wild!

You feel guilty ordering a 20 ounce steak – think about it in kg instead

20oz------ 1

28.35gx ------- 1 oz

1 kgx ---- = 1000g

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Scientific NotationDigits plus the power of 10

700 is a number

Thus, 700 is the same as 7.0 x 102

700 can be restated as 7.0 x 100

100 can be restated as 10 x 10

10 x 10 can be stated as 10 2

The moon is more than 384 thousand km from earth.

Ex: Windsor to Disneyland is 745km, or 7.45 x 102

(700.0 is the same number)