- 1). Recall the Origin of the Decimal System
Realize that counting, which is basic to math, is a natural human activity. In the beginning we used our fingers and perhaps our toes to count. The fact that we had 10 fingers and 10 toes influenced our development of the decimal system. First fully developed in India many centuries ago, the decimal system made its way to China and then to the Arabs in the first millennium AD, who transmitted to us the decimal system and the Arabic numerals that we use today. The great Italian mathematician Fibonacci introduced the decimal system to Europe around 1200 AD. - 2). Master the Essence of the Decimal System
Practice thinking about the powers (exponents) of 10, which are the essence of the decimal system. The decimal system is a positional notation system in math that uses the base of ten and powers of 10 to represent numbers, large and small. The decimal point divides numbers that are larger than one to the left from numbers smaller than one (also called decimal fractions) to the right of the decimal point.
Remember that different positions of numbers are meaningful and represent powers of 10. For example, the number 486 has 4 in the hundreds place (10 to the 2nd power) and means 400. The 8 is in the tens position and represents 8 x "10 to the first power," or 80. The 6 is in the units position and represents 10 raised to the zero power, or 1, so it is 6 x 1 which equals six. (In math, any number raised to the zero power equals one -- by definition.)
Numbers to the right of the decimal point are less than one and are different negative powers of 10 depending on position. So you have the tenths place, hundredths place, thousandths place and so on, to the right of the decimal point (10 to the minus 1 power, 10 to the minus 2nd power, and 10 to the minus 3rd power, respectively). Isn't math interesting?
10 to the minus 1 power = 1/10.
10 to the minus 2nd power = 1/100.
10 to the minus 3rd power = 1/1,000. - 3). Study the Decimal System So That You Can Teach It
The best way for you to really master the decimal system and the use of decimals in math is to learn it well enough to teach it to preteens. This means striving to understand the "why" of every aspect of decimals in math as well as how to apply and use them. Visit some of the math teaching sites on the web to get insight and practice from multiple perspectives. Write down any elements that are challenging for you. Many people have difficulty with the concept of negative powers of 10. Stick with it. - 4). Apply Decimals in Real Life Situations
You use decimals every time that you use cash. Currencies are excellent examples of decimal applications of math. The cents are the decimal fractions to the right of the decimal point. So 36 cents is $.36. When adding expense amounts all the items must have their decimal points aligned in a column for adding by hand. Also use the metric system as often as you can because it is a decimal system, too. Centimeters, millimeters, kilometers are all powers of 10 applied to the base unit of the meter. Good luck!
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