Category Science

WHAT ARE DECIMAL NUMBERS?

Decimal numbers use 10 digits, which are combined to make numbers of any size. The position of the digit determines what it means in any number. For example, the 2 in the number 200 is ten times the size of the 2 in the number 20. Each position of a number gives a value ten times higher than the position to its right. So 9867 means 7 units, plus 6 x 10, plus 8 x 10 x 10, plus 9 x 10 x 10 x 10. As decimal numbers are based on the number 10, we say that this is a base -10 number system.

We have learnt that the decimals are an extension of our number system. We also know that decimals can be considered as fractions whose denominators are 10, 100, 1000, etc. The numbers expressed in the decimal form are called decimal numbers or decimals.

For example: 5.1, 4.09, 13.83, etc.

A decimal has two parts:

(a) Whole number part

(b) Decimal part

These parts are separated by a dot (.) called the decimal point.

  • The digits lying to the left of the decimal point form the whole number part. The places begin with ones, then tens, then hundreds, then thousands and so on.
  • The decimal point together with the digits lying on the right of decimal point form the decimal part. The places begin with tenths, then hundredths, then thousandths and so on…

Example:

(i) In the decimal number 211.35; the whole number part is 211 and the decimal part is .35

(ii) In the decimal number 57.031; the whole number part is 57 and the decimal part is .031

(iii) In the decimal number 197.73; the whole number part is 197 and the decimal part is .73

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WHAT IS THE BINARY SYSTEM?

The binary system is another way of counting. Instead of being a base-10 system, it is a base-2 system, using only two digits: 0 and 1. Again, the position of a digit gives it a particular value. 1010101 means 1 unit, plus 0 x 2, plus 1 x 2 x 2, plus 0 x 2 x 2 x2, plus1 x 2 x 2 x 2 x 2, plus 0 x 2x 2 x 2 x 2x 2,plus 1 x 2 x 2 x 2 x 2 x 2 x 2. 1010101 is the same as 85 in decimal numbers.

When you learn math at school, you use a base-10 number system. That means your number system consists of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When you add one to nine, you move the 1 one spot to the left into the tens place and put a 0 in the ones place: 10. The binary system, on the other hand, is a base-2 number system. That means it only uses two numbers: 0 and 1. When you add one to one, you move the 1 one spot to the left into the twos place and put a 0 in the ones place: 10. So, in a base-10 system, 10 equal ten. In a base-2 system, 10 equal two.

In the base-10 system you’re familiar with, the place values start with ones and move to tens, hundreds, and thousands as you move to the left. That’s because the system is based upon powers of 10. Likewise, in a base-2 system, the place values start with ones and move to twos, fours, and eights as you move to the left. That’s because the base-2 system is based upon powers of two. Each binary digit is known as a bit.

Don’t worry if the binary system seems confusing right now. It’s fairly easy to pick up once you work with it a while. It just seems confusing at first because all numbers are made up of only 0s and 1s. The familiar base-10 system is as easy as 1-2-3, while the base-2 binary system is as easy as 1-10-11.

You may WONDER why computers use the binary system. Computers and other electronic systems work faster and more efficiently using the binary system, because the system’s use of only two numbers is easy to duplicate with an on/off system. Electricity is either on or off, so devices can use an on/off switch within electric circuits to process binary information easily. For example, off can equal 0 and on can equal 1.

Every letter, number, and symbol on a keyboard is represented by an eight-bit binary number. For example, the letter A is actually 01000001 as far as your computer is concerned! To help you develop a better understanding of the binary system and how it relates to the decimal system you’re familiar with, here’s how the decimal numbers 1-10 look in binary:

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HOW ARE ROMAN NUMERALS USED?

The romans had a number system with a base of 10, as we do, but they used different numerals to write it down. For the numbers one to nine, instead of using nine different numerals, they used only three different letters, combining them to make the numbers. This made it very difficult for them to do even simple calculations, so their advances in mathematics and related fields were not as great as might have been expected from such a far-reaching civilization.

Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet. Modern usage employs seven symbols, each with a fixed integer value:

The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced in most contexts by the more convenient Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some minor applications to this day.

One place they are often seen is on clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as:

I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII

The notations IV and IX can be read as “one less than five” (4) and “one less than ten” (9), although there is a tradition favoring representation of “4” as “IIII” on Roman numeral clocks.

Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs. MCM, signifying “a thousand, and a hundred less than another thousand”, means 1900, so 1912 is written MCMXII. For the years of this century, MM indicates 2000; so that the current year is MMXX (2020).

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DOES THE WHOLE WORLD USE THE GREGORIAN CALENDAR?

For international communications, the whole world does use the Gregorian calendar, but other religious and traditional calendars are still in use around the world. The Jewish calendar has a year that varies between 353 and 385 days. The Muslim calendar has 354 or 355 days in a year.

Religious, administrative and social functions in any country or organization requires a systematic organization of days in the form of a calendar. Calendars designate dates to particular days. Civil calendars are utilized for purposes that are administrative and official in a nation. More often than not, the civil calendars are also used by the general population in their day to day planning. The Gregorian calendar, used across the globe, is believed to be the most extensively relied on civil calendar. Many countries, Christian or not, all over the world have adopted this civil calendar despite its strong association with the Catholic Church. There however are countries which have their own calendars for civil reasons. These countries completely rely on a completely different calendar, either alongside the Gregorian one or in entirety. Some of these civil calendars are a mere modification of the Gregorian calendar.

Iran and Afghanistan share the Solar Hijri calendar for administrative and religious purposes. They do not use the Gregorian calendar at all. This is the same case with Nepal and Ethiopia which exclusively use the Vikram Samvat calendar and the Ethiopian calendar respectively. The Ethiopian calendar has a close correlation with the Egyptian calendar from which it is derived. It is a solar calendar with 29th August or 30th August as the date the year begins in the Ethiopian calendar. Between the Gregorian and the Ethiopian calendars, there exists a 7 to 8 years gap.

For ease of understanding throughout the world, there exists a means of expressing dates from these civil calendars relative to the Gregorian calendar dates.

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WHAT IS GREENWICH MEAN TIME?

Greenwich Mean Time is the local time at the Greenwich Observatory in London, England. The line of 0° longitude, along which the Sun passes overhead exactly at noon, runs through the Observatory. Greenwich Mean Time (GMT, also known as Universal Time, or UT) is used as a standard time all over the world.

Greenwich Mean Time (GMT) is the mean solar time at the Royal Observatory in Greenwich, London, reckoned from midnight. At different times in the past, it has been calculated in different ways, including being calculated from noon; as a consequence, it cannot be used to specify a precise time unless a context is given.

English speakers often use GMT as a synonym for Coordinated Universal Time (UTC). For navigation, it is considered equivalent to UT1 (the modern form of mean solar time at 0° longitude); but this meaning can differ from UTC by up to 0.9 s. The term GMT should not thus be used for certain technical purposes requiring precision.

Because of Earth’s uneven angular velocity in its elliptical orbit and its axial tilt, noon (12:00:00) GMT is rarely the exact moment the Sun crosses the Greenwich meridian and reaches its highest point in the sky there. This event may occur up to 16 minutes before or after noon GMT, a discrepancy calculated by the equation of time. Noon GMT is the annual average (i.e. “mean”) moment of this event, which accounts for the word “mean” in “Greenwich Mean Time”.

Originally, astronomers considered a GMT day to start at noon, while for almost everyone else it started at midnight. To avoid confusion, the name Universal Time was introduced to denote GMT as counted from midnight. Astronomers preferred the old convention to simplify their observational data, so that each night was logged under a single calendar date. Today, Universal Time usually refers to UTC or UT1.

The term “GMT” is especially used by bodies connected with the United Kingdom, such as the BBC World Service, the Royal Navy, and the Met Office; and others particularly in Arab countries, such as the Middle East Broadcasting Center and OSN. It is a term commonly used in the United Kingdom and countries of the Commonwealth, including Australia, New Zealand, South Africa, India, Pakistan, Bangladesh and Malaysia; and in many other countries of the Eastern Hemisphere.

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WHAT WERE THE FIRST CLOCKS LIKE?

It was probably the Babylonians who first divided the day into 24 hours, with 60 minutes in each hour. These are numbers that can easily be divided by 2, 3 and 4. The very first clocks, like the first calendars, were based on the Sun, using the movements of its shadow to read the time from a marked area of Earth or stone. Later methods of time measurement were based on actions that happened at a fixed rate, such as the pull of gravity on grains of sand.

For thousands of years, devices have been used to measure and keep track of time. The current sexagesimal system of time measurement dates to approximately 2000 bc from the Sumerians. The Egyptians divided the day into two 12-hour periods, and used large obelisks to track the movement of the sun. They also developed water clocks, which were probably first used in the Precinct of Amun-Re, and later outside Egypt as well; they were employed frequently by Persians and the Ancient Greeks, who called them clepsydrae. The Zhou dynasty is believed to have used the outflow water clock around the same of the time, devices which were introduced from Mesopotamia as early as 2000 bc.

Other ancient timekeeping devices include the candle clock, used in ancient China, ancient Japan, England and Mesopotamia; the time-stick, widely used in Persia, India and Tibet, as well as some parts of Europe; and the hourglass, which functioned similarly to a water clock. The sundial, another early clock, relies on shadows to provide a good estimate of the hour on a sunny day. It is not so useful in cloudy weather or at night and requires recalibration as the seasons change (if the gnomon was not aligned with the Earth’s axis).

The earliest known clock with a water-powered escapement mechanism, which transferred rotational energy into intermittent motions, dates back to 3rd century bc in ancient Greece; Chinese engineers later invented clocks incorporating mercury-powered escapement mechanisms in the 10th century, followed by Arabic engineers inventing water clocks driven by gears and weights in the 11th century.

The first mechanical clocks, employing the verge escapement mechanism with a foliot or balance wheel timekeeper, were invented in Europe at around the start of the 14th century, and became the standard timekeeping device until the pendulum clock was invented in 1656. The invention of the mainspring in the early 15th century allowed portable clocks to be built, evolving into the first pocket watches by the 17th century, but these were not very accurate until the balance spring was added to the balance wheel in the mid-17th century.

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