Standards of Measure - Weebly



1.1 – Standards of Measure

• Standards of measure are sets of units of measure for length, weight, and other quantities defined in a way that is useful to a large number of people.

• US (Customary) System vs. SI (Metric) System

o The Metric System has been widely accepted throughout the world, and has even been adopted by some industries in the US. The United States is continuing to hold onto and use the US System. Therefore, it is important that we learn and understand both, and know how to convert between the two.

o RECALL: NASA lost a $125 million Mars climate orbiter when units were not properly converted.

1.2 – Metric System

• The metric system is a decimal, or base of 10, system. It is easy to use because the calculations are based on the number 10 and its multiples. Special prefixes are used to name these multiples and submultiples, which may be used with most all SI units. (See the table handout.)

Ex. 1:

Write the SI abbreviation for 36 centimeters.

Ex. 2:

Write the SI metric unit abbreviation for 45 kg.

➢ The basic metric unit of length is _________________________.

➢ The basic unit of mass is ________________________________.

➢ Two common units of volume are _________________ and _________________.

➢ The basic metric unit of time is ________________________.

• Conversion Factors: Expression used to change from one set of units to another. The conversion factor is set up so that the old units cancel each other out.

1.3 – Length

• Metric Length: The current definition of a meter is – the length of path traveled by light in a vacuum during a time interval of 1/299,792,458 of a second.

➢ Long distances are measured in ______________________ (_______).

➢ Short distances are measured in ______________________ (_______).

➢ Very small lengths are measured in ______________________ (_______).

• Visualizations:

Ex. 1:

Change 215 cm to meters (m).

[pic]

Ex. 2:

Change 39.5 mm to centimeters (cm).

Ex. 3:

Change 0.05 km to centimeters (cm).

• US Length: The basic unit of the US system is the foot.

• Metric - US Conversions:

Ex. 1:

Express 10 inches in centimeters.

[pic]

Ex. 2:

Change 15 miles to kilometers.

Fill in the blank with the most reasonable metric unit (km, m, cm, or mm).

➢ Your car is about 6 __________ long.

➢ The ceiling in your bedroom is about 240 __________ high.

➢ Juan drives 9 __________ to school everyday.

➢ A newborn baby is about 45 __________ long.

1.4 – Area and Volume

• Area: The number of square units that a figure contains. Standard units are based on the square and are called square inches, square centimeters, square miles, etc.

Ex. 1:

Find the area of a rectangle 2 cm long and 4 cm wide.

[pic]

Ex. 2:

Find the area of the metal plate shown below.

Ex. 4:

Find the area of the figure.

• Cross-sectional Area: The surface that would be seen by butting a geometric solid with a thin plate parallel to one side of the solid.

Ex. 4:

Find the cross-sectional area of the I-beam.

• Volume: The number of cubic units that a figure contains. Standard units are based on the cube and are called cubic inches, cubic centimeters, cubic yards, etc.

➢ A common unit of volume in the metric system is the liter (L). The liter is commonly used for liquid volumes.

➢ Important relationship between the liter and cubic centimeter:

➢ 1 L = _________ cm3

➢ _______ L = 1 cm3

➢ 1 mL = _________ L

➢ _______ mL = ________ cm3

Ex. 5:

Find the volume of the prism shown.

1.5 – Mass and Weight

• Mass: The mass of an object is the quantity of material making up the object. One unit of mass in the metric system is the gram. The gram is defined as the mass of 1 cubic centimeter (cm3) of water at its maximum density.

➢ Since the gram is so small, the ______________________ (_______) is the basic unit of mass in the metric system.

➢ The __________________________ (1,000______) is used to measure the mass of very large quantities such as the coal on a barge, a trainload of grain, or a shipload of ore.

➢ Very small masses, such as medicine dosages, are measured using the

______________________ (_______).

• Visualizations:

• Weight: The weight of an object is the measure of the gravitational force or pull acting on it. The Newton is the metric unit of weight. The pound is the US unit of force or weight.

➢ 1 N = _________ lb

➢ 1 lb = _________ N

Fill in the blank with the most reasonable metric unit (kg, g, mg, or metric ton).

➢ A newborn’s mass is about 3 __________.

➢ A candy recipe calls for 175 __________ of chocolate.

➢ I bought a 5-__________ bag of potatoes at the store today.

1.6 – Accuracy, Precision, and Significant Digits/Figures

• The accuracy of a measurement refers to the number of significant digits/figures. It describes how well the results of an experiment agree with the standard value.

• Significant digits (or figures) are the number of units that we are reasonably sure of having counted when making a measurement. The greater the number of significant digits given in a measurement, the better the accuracy and vice versa.

o To Find the Number of Sig Figs:

1) All nonzero digits are significant.

2) Zeros are significant when they

a. are between significant digits;

b. follow the decimal point and a significant digit; or

c. are in a whole number and a bar is placed over the zero.

• The precision of a measurement refers to the smallest unit with which a measurement is made, that is, the position of the last significant digit. It describes the degree of exactness of a measurement.

Ex. 1:

Determine the accuracy (number of sig figs) and precision of each measurement.

(a) 536 ft; (b) 5007 m; (c) 0.02700 g; (d) [pic] g; (e) 1.20 ( 10-5 ms; (f) 70.00 m2

|Problem |Accuracy (No. of Sig Figs) |Precision (Loc. of Last Sig Fig) |

|(a) 536 ft |3 |1 ft |

|(b) 5007 m |4 (both zeros are significant) |1 m |

|(c) 0.02700 g |4 (only the right two zeros are |0.00001 g |

| |significant) | |

|(d) [pic] g |2 (only the first zero is significant) |10 m |

|(e) 1.20 ( 10-5 ms |3 (the zero is significant) |0.01 ( 10-5 ms or 0.0000001 ms |

|(f) 70.00 m2 |4 (all zeros follow a sig fig) |0.01 m2 |

Ex. 2:

In the following set of measurements, find the measurement that is (a) the most accurate and (b) the most precise.

{15.7 in.; 0.018 in.; 0.07 in.}

| |Accuracy |Precision |Answer to Problem |

|15.7 in. | | | |

|0.018 in. | | | |

|0.07 in. | | | |

1.7 – Calculations with Measurements

• The sum or difference of measurements can be no more precise than the least precise measurement.

o To Add or Subtract Measurements:

1) Make certain that all the measurements are expressed in the same unit. If they are not, convert them all to the same unit.

2) Add or subtract.

3) Round the results to the same precision as the least precise measurement.

Ex. 1:

Add the measurements 1370 cm, 1575 mm, 2.374 m, and 8.63 m.

• The product or quotient of measurements can be no more accurate than the least accurate measurement.

o To Add or Subtract Measurements:

1) Multiply or divide the measurements as given.

2) Round the results to the same number of sig figs as the measurement with the lease number of sig figs.

Ex. 2:

Find the value of [pic].

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