REVIEW….

Introduction: Science is a process of measuring, understanding, and communicating natural phenomenon. In the United States and around the world, scientists use the metric system because it is a decimal system (based on 10) that is easy to understand, convert, and use. The metric system has a basic unit for each type of measurement. The gram measures mass. The meter measures length. The liter measures volume. These correlate to ounces, feet, and quarts in the English system. We can add prefixes to describe each decimal factor of the base units:

SI prefixes

Factor Name Symbol

1024yottaY

1021zettaZ

1018exaE

1015petaP

1012teraT

109gigaG

106mega M

103kilok

102hectoh

101dekada

Factor Name Symbol

10-1decid

10-2centic

10-3millim

10-6microµ

10-9nanon

10-12picop

10-15femtof

10-18attoa

10-21zeptoz

10-24yoctoy

Luckily, we will only focus on those italicized and bolded! kilo- stands for 1000, hecto- means 100, deka- is 10, deci- is 0.1, centi- means 0.01, and milli- represents 0.001. The base unit is 1. When the prefix is present, there are that many of the base units. One way to represent this idea is the Metric Staircase:

You will use the prefix table and the metric staircase along with some simple materials to complete this activity.

Convert the following BASIC units:

  1. 56 m = ______cm
  2. 424 mm = ______cm
  3. 702 cm = ______m
  4. 1254 ml = ______l
  5. 245 l = ______ml
  6. 3.2 kg = ______g
  7. 567 mg = ______g
  8. 34 km = ______m
  9. 3.56 kg = ______hg
  10. 322 m = ______km
  11. 0.047 l = ______ml
  12. 718 cm = ______dam
  13. 0.78 g = ______mg
  14. 0.079 dg = ______cg
  15. 3.98 mm = ______m
  16. 0.069 hl = ______cl

Converting Areas:

Square Meter = The square meteris thebasic unit of areaof the Metric System. Area is length by width, so, a square that is 1 meter on each side is1 square meter.The Unit ismeters × meters, which is writtenm2(square meters).You could have other shapes (such as a rectangle that is ½ a meter by 2 meters) that also make 1 square meter.

Example: How big is this rectangle?

It is 2m by 3m, so it is 2m*3m=6m2

Square Millimeter = A square millimeter ismillimeters × millimeters, which is written mm2.A millimeter is one-thousandth of a meter (1/1000 or 0.001 meter), so a square millimeter is

0.001 m * 0.001 m = 0.000001 m2

In other words a square millimeter isone-millionthof a square meter.So, a square meter has 1,000,000 square millimeters.

Square Centimeter = A square centimeter iscentimeter × centimeter,cm2. A centimeter is one-hundredth of a meter (1/100meter), so a square centimeter is also:

0.01m * 0.01m = 0.0001m2

In other words a square centimeter isone-ten-thousandthof a square meter.So a square meter has 10,000 square centimeters.

The Hectare = A hectare (ha) is an area equal to a square that is 100 meters on each side.So a hectare has 100 m × 100 m = 10,000 m2(square meters).

Hectares are commonly used to measure land.

Square Kilometer

A square kilometer iskilometer × kilometer, which is written km2.

A kilometer is a thousand meters, so a square kilometer is also:1,000 m × 1,000 m = 1,000,000 m2(square meters)

In other words a square kilometer isone-millionsquare meters.Square kilometers are commonly used to measure large areas of land.

Some Examples

A square meter is about half the area of a doorway or the area covered by a large umbrella

A hectare is about:

  • two and a half acres
  • 2.471 acres (to 3 decimal places)
  • 100,000 square feet
  • more precisely 107,639 square feet

Some Practice Problems…

  1. 9 dam2 = ______hm2
  2. 580 mm2 = ______m2
  3. 270 mm2 = ______cm2
  4. 630 m2 = ______dam2
  5. 0.75 hm2 = ______cm2
  6. 0.05 dm2 = ______mm2
  7. 64 km2 = ______dam2
  8. 144 m2 = ______km2
  9. 36cm2 = ______dm2
  10. 121cm2 = ______m2

Converting Volumes:

Cubic Meter = Thecubic meteris one unit of volume of the Metric System. Volume is length by width by height, so, acube that is 1 meter on each side is1 square meter.The Unit ismeters × meters x meters, which is writtenm3(cubic meters).You could have other shapes (such as a rectangular cube that is ½ meter by 2 meters by 1 meter) that also make 1 square meter.

THERE ARE 1000 liters in 1 m3!

How big is this stack of boxes if each box is one cubic meter?

2m * 4m * 4m = 32 m3

Cubic millimeter = A cubic millimeter ismillimeters × millimeters × millimeters, which is written mm3.A millimeter is one-thousandth of a meter (1/1000 or 0.001 meter), so a cubic millimeter is

0.001 m * 0.001 m * 0.001 m = 0.000000001 m2

In other words a cubic millimeter isone-billionthof a cubic meter.So, a cubic meter has 1,000,000,000 square millimeters.

Cubic Centimeter = A square centimeter iscentimeter ×centimeter × centimeter = cm3. A centimeter is one-hundredth of a meter (1/100meter), so a cubic centimeter is also:

0.01m * 0.01m * 0.01m = 0.000001m3

In other words a cubic centimeter isone-millionthof a cubic meter.So a cubic meter has 1,000,000 cubic centimeters.

COOL FACT: 1 cm3 = 1 ml (common dosage of medicine).

Some Practice Problems…

  1. 26 m3 = ______hm3
  2. 1400 mm3 = ______m3
  3. 15 dm3 = ______cm3
  4. 32,546 m3 = ______km3
  5. 0.27 cm3 = ______mm3
  6. 5 dam3 = ______dm3
  7. 144 km3 = ______m3
  8. 1000 hm3 = ______km3
  9. 936 cm3 = ______m3
  10. 512 mm3 = ______m3

Converting Temperatures:

From / To Fahrenheit / To Celsius / To Kelvin
Fahrenheit (F) / F / (F-32)/1.8 / (F-32)/1.8 + 273.15
Celsius (C) / (C*1.8)+32 / C / C+273.15
Kelvin (K) / (K-273.15) * 1.8 + 32 / K-273.15 / K
Use the equations above to convert the following values into the other temperature units.
212 F
37 C
273.15 K
70 F
-273.15