# The A to Z of mathematics a basic guide - Sidebotham T.H.

ISBN 0-471-15045-2

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♦ Cubic millimeters are used to measure very small volumes, like the volume of a garden pea, say 250 mm3.

♦ Cubic centimeters are used to measure medium-sized volumes, like the volume of a tennis ball, say 750 cm3.

♦ Cubic meters are used to measure large volumes, like the volume of a bedroom, say 32 m3.

The relationships between them are

1000 mm3 = 1 cm3

1,000,000 cm3 = 1m3

The fact that 1 million cubic centimeters = 1 cubic meter is particularly interesting, because it gives us an idea about how big a million is. Another interesting fact is that 1 ml of water weighs 1 g at a temperature of 4°C.

Mass The units of mass are:

♦ Milligrams (mg), which used to measure the mass of very small quantities, like the mass of a pin.

♦ Grams (g), which used to measure the mass of small quantities, like the mass of a ballpoint pen, say 25 g.

♦ Kilograms (kg), which are used to measure the mass of larger quantities, like the mass of a sack of potatoes, say 20 kg.

♦ Tonnes (t), which are used to measure the mass of very large quantities, like the mass of a truckload of wood, say 2 t (for the relationship between tonnes and U.S. tons, see the entry Gram).

MIDORDINATE RULE 289

The relationships between them are

1000 mg = 1 g

1000 g = 1 kg

1000 kg = 11

Example. Convert the mass of a truckload of wood of 2.4 tonnes to kilograms. Solution. We multiply the number of tonnes by 1000 to convert to kilograms:

2.4 x 1000 = 2400

The mass of the truck of wood is 2400 kg.

References: Système International d’Unités, SI Units.

MIDORDINATE RULE

This is a rule for finding the approximate area between a curve and the x-axis. The process is explained in the example.

Example. Find the approximate area in the figure of the region enclosed by the curve y = x2, the x-axis, and the vertical lines x = 1 and x = 2.

Solution. The region is shaded in the figure. The dashed line is a vertical line through the point x = 1.5, which is midway along the width of the shaded strip. The length of the dashed line, called the midordinate, is found by substituting x = 1.5 into the equation of the curve y = x2.

y = (1-5)2 y = 2.25

290 MILLILITER

The coordinates of the point where the dashed line meets the curve are (1.5, 2.25). Now write

Approximate area of shaded region = width of region x value of midordinate of

the region

= 1 x 2.25

= 2.25

The approximate area of the shaded region is 2.3 square units, to 1 dp. A more accurate result can be obtained by splitting the shaded area into two or more strips and using the midordinate rule on each strip. The greater the number of strips, the more accurate is the answer.

A closer look at the process will reveal that the midordinate method is based on regarding the shaded area as a trapezium and then finding its area.

Reference: Trapezium.

MILE

The mile is a measurement of length and is an imperial unit. One mile is approximately 1.609 kilometers, or 1609 meters. An approximate guide for quick conversions between the two units is to say that 5 miles is equivalent to about 8 km.

References: Imperial System of Units, Kilometer, Metric Units.

MILLI

This is a prefix meaning one-thousandth (1/1000) part of some quantity. For example, one-thousandth part of a meter is called a millimeter, which is abbreviated mm. In this abbreviation, the first m stands for milli and the second m stands for meter. The metric units are mainly based on dividing some quantity by 1000 (prefix milli) or multiplying some quantity by 1000 (prefix kilo).

References: Meter, Metric Units, Millimeter, SI Units.

MILLILITER

One milliliter is 1/1000 of a liter, and is abbreviated ml. One milliliter is the same size as 1 cubic centimeter (cm3) and is a useful unit for measuring medicine. A teaspoon of medicine is about 5 ml.

References: Metric Units, Milli.

MIRROR LINE 291

MILLIMETER

One millimeter is 1/1000 of a meter, and is abbreviated mm. The first m stands for milli and the second m stands for meter. Builders and architects use millimeters as the unit for measuring distances in preference to centimeters. If you are measuring and cutting wood to build a house, the most accuracy you can expect is to the nearest millimeter.

References: Metric Units, Milli.

MINIMUM VALUE

Reference: Maximum Value.

MINOR ARC

Reference: Arc.

MINOR SECTOR

Reference: Sector of a Circle.

MINOR SEGMENT

Reference: Segment of a Circle.

MINUTE

There are two uses for the unit minute:

1. A minute is an extremely small angle, and is 1/60 of 1 degree. Written as a decimal, 1 minute = 0.017 degree, to 3 dp. The symbol for 1 minute is l7.

2. A minute is also a measure of time, and is 1/60 of 1 hour. One minute is 0.017 hour, to 3 dp. The minute is subdivided again into seconds, where 1 second is 1/60 of 1 minute. This means that there are 60 seconds in 1 minute, 60 minutes in 1 hour, and 3600 seconds in 1 hour.

Reference: Degree.

MIRROR LINE

If an object is reflected in a mirror to produce an image, then the object and the image are mirror images of each other. In the drawing figure, m is the mirror line, the flag F is the object, and the image is the flag F'. The mirror line is also known as the axis of symmetry of the whole drawing, and is called the mediator of the two flags.

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