In the sciences, the magnitude of earthquakes is measured in terms of the Richter scale, oven and room temperatures are measured with a thermometer, and water hardness is measured in terms of mineral content. In this module you will explore the development of measurements, from the non-standard units to the current international system of units. The cycles of the sun, moon and other celestial bodies were used for time measurements.
International Bureau of Weights and Measures (BIPM) to oversee the activities of the national standards laboratories. In 1971, another basic unit was added - the mole as the basic unit for the amount of material. This system is the modern form of the metric system and is the most widely used measurement system.
It establishes a set of prefixes for unit names and unit symbols that can be used when specifying multiples and fractions of units. So, to convert from one unit to another, we can multiply by one of the conversion factors without changing the value. Another way of converting metric measures from one unit to another is by shifting/moving the position of the decimal point in the measure.
Identify the appropriate measuring instrument and metric unit to use in solving each of the following problems.
Measuring Weight/Mass and Volume
The kilogram is the base unit of mass in the metric system, while in the English system of measurement the base unit of mass/weight is the pound (lb). Light objects are measured in milligrams or grams, while heavy objects are measured in kilograms or pounds. The units of mass in the metric system have the same prefixes as the units of length.
It is measured by the number of cubic units or the amount of liquid it can hold. The most commonly used metric units for volume of solids are the cubic meter (m3) and the cubic centimeter (cm3 or cc) while the most commonly used metric units for volume of liquids are the liter (L) and the milliliter (ml). The units of volume in the metric system have the same prefixes as the units of length.
In the English system of measurement, the commonly used units for volume of solids are cubic feet (ft3) and cubic inches (in3), while for liquid volume are pint, quart, and gallon. 675 ml = 0.675 L Move the decimal point the same number of places and in the same direction.
Fundamental Algebra
Constants, Variables, and Algebraic Expressions
The term –y has no obvious numerical coefficient, but that does not mean that it has no numerical coefficient. Also note that the first and last algebraic expressions have two terms, while the second has three terms. To evaluate an algebraic expression is to substitute given specific values for the variables and then simplify the resulting numerical expression.
This means you take the sum of twice the length and twice the width of the rectangle to calculate the perimeter.
English Phrases and Mathematical Phrases
The following table shows some English expressions related to addition, subtraction, multiplication and division and their corresponding translations in mathematics or algebra. It is important to note that the order of constants and variables cannot be changed when subtracting and dividing.
Polynomials
The degree of a term that has more than one variable is the sum of the exponents of the variables. The degree of a polynomial is the highest exponent or the highest sum of exponents of the variables in a term. A polynomial is a type of algebraic expression that represents a sum of one or more terms containing integer exponents in the variable.
A polynomial is in standard form if its terms are arranged from the term with the highest degree, up to the term with the lowest degree.
Laws of Exponents
What do you notice about the exponents of the factors and the exponent of the products? What do you notice about the exponents of the dividends and the divisors and the exponent of the multiplier? Did you notice that the product of the powers of the base is equal to the exponent of the product.
To find the power of a product, raise each factor to the given power and then multiply the resulting powers. To find the power of a quotient, raise the quotient and divisor to the given power and then divide the resulting powers.
Addition and Subtraction of Polynomials
To combine like terms, take the sum of the numerical coefficients and annex the same literal coefficients. If there is more than one term, for convenience, write similar terms in the same column. Recall that subtraction can be defined in terms of addition.a – b = a + (-b) In other words, subtraction is the same as adding the opposite of the subtrahend.
To subtract polynomials, change the sign of the denominator and proceed to the addition rule.
Multiplying Polynomials
To multiply a monomial by a polynomial, simply apply the distributive property and follow the rule for multiplying monomial by a monomial. To multiply a binomial by another binomial, simply divide the first term of the first binomial over each term of the second binomial and then divide the second term over each term of the other binomial and simplify the results by comparing combine terms. To multiply a polynomial with more than one term by a polynomial with three or more terms, simply divide the first term of the first polynomial over each term of the other polynomial.
Repeat the procedure until the last term and simplify the results by combining like terms.
Dividing Polynomials
To divide a polynomial by a polynomial with more than one term (by long division), simply follow the procedure for dividing numbers by long division. Set up long division by writing the division symbol, where the divisor is outside the division symbol and the dividend inside it. Multiply the first term of the answer by the divisor and subtract the results from the first two terms of the polynomial.
Continue dividing, multiplying, and subtracting until the remainder is in a power like the variable in the first term of the divisor. She wanted the length of the blanket to be 1 foot longer than twice the width, otherwise her toes get cold. If the area covered by the quilt is 28 square feet, how long is the quilt.
Special Products
- PRODUCT OF TWO BINOMIALS
- PRODUCT OF THE SUM AND DIFFERENCE OF TWO TERMS The product of the sum and difference of two terms is equal to
- SQUARE OF A BINOMIAL To square a binomial
- CUBE OF A BINOMIAL To cube a binomial
- PRODUCT OF A BINOMIAL AND A TRINOMIAL To find the product of a binomial and a trinomial
PRODUCT OF THE SUM AND DIFFERENCE OF TWO TERMS The product of the sum and the difference of two terms is equal to The product of the sum and the difference of two terms is equal to the difference of the squares of the terms. The most commonly used measurement system is the SI system, the modern form of the metric system. Accuracy of all calculations All calculations Most are correct and are correct.
