In scientific notation, this number is written as 3 x 108. The speed of light, a constant in the universe frequently employed in physics, is approximately 300,000,000 meters per second. Here are some examples of scientific notation: Thus, scientific notation will be expressed as a x 10b with a always being a number between one and ten. Scientific notation makes these numbers easier to use by requiring that the first number (called the coefficient or the significand) is always between 1 and 10, The second number (called the base) is expressed as a power of 10. Scientists often must use very large or very small numbers. Recall that any number to the power of 1 is equal to itself and any number to the power of 0 is equal to 1.Ī number can be written several different ways using exponents of the base 10. In the films both the outward and the inward journeys quickly reach scales which would be rather complicated to express in writing without using exponential notation of the “powers of ten.”Īny number of the decimal numeral system can be represented as a sum of powers of ten multiplied by the value of its digits:ġ,354.95 = 1 x 103 + 3 x 102 + 5 x 101 + 4 x 100 + 9 x 10-1 + 5 x 10-2 Exponential notation is also an advantage for very small numbers: 10-6 is a short way to represent one millionth, or 0.000001. This number can also be written as 1/100 or 0.01. Note how the exponent corresponds to the number of zeros to the right of the “1.” Numbers smaller than one can also be represented by powers of ten, using negative exponents, as a negative power means how often the number one is divided by itself: 10-2 equals 1/10 times 1/10, which is one divided twice by 10. But take one million: 106 is definitely shorter to write than 1,000,000. 102 is the same as 100, without any obvious advantage in writing it either way (three symbols are required in both cases). The exponent indicates how many times to multiply a number by itself. Exponents, written as a superscript after the symbol, are a simpler way to express these numbers, e.g. When very large or very small numbers are required, the place value system becomes difficult to use. 101 means one-hundred and one, one thousandths or one tenth plus one one-thousandth. The first place to the right of the decimal, includes symbols whose value is divided by ten, the second place to the right of the decimal is for symbols whose value is determined by dividing by 100, and so on. The same procedure works in reverse for numbers smaller than one. Every student knows how this works, but it is important to recall the underlying rationale in order to understand the meaning of exponents and the different numeral systems that will be discussed below. Counting is continued by starting over again with the other two positions (101,102, 103, etc.). By 99, all possible combinations of symbols in two positions have been used, and a new position to the left is created in which the symbol occupying that place is multiplied by 100. When twenty is reached, the symbol to the left (the one multiplied by 10) changes to “2,” and the first position then runs from 0 to 9, representing the numbers 20 to 29, and so on. In this manner a representation for numbers 10 – 19 is obtained. When ten is reached, the smallest non-zero symbol, “1”, is placed into this new position, letting the first position run again from 0 to 9. The chosen way to count numbers after 9 is to use a second position to the left to represent numbers multiplied by ten. Having ten basic numbers or symbols, one of which represents nothing or zero, means that numbers greater than nine can be expressed only by combining symbols in some manner. This numeral system is called the Decimal Numeral System (deci being Latin for ten). Contemporary systems of counting have gone far beyond Roman numerals and there is no finger on a hand that corresponds to the symbol “0.” However, the most prevalent numeral system still uses precisely ten symbols. Two such hands united by crossed wrists make an “X”, the Roman numeral for ten. However, a common sense folk etymology for Roman numerals attributes the Roman numeral “I” to the shape of a single finger and the Roman numeral “V” to a hand with five outstretched fingers. The most accepted theory on Roman numerals is that they evolved from Etruscan symbols. In fact, this has been done since counting became part of human culture. Small children use their fingers to count, add, and subtract. The modern system of counting using precisely ten symbols appears to relate to the fact that human hands have ten fingers. FICTION (SOAPS, DRAMAS, AND REALITY/SURVIVAL SHOW).FILM ADAPTATIONS OF NOVELS, SHORT STORIES, OR PLAYS.TALKING AND PLAYING WITH MOVIES: AGES 3-8.
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