Today's soundtrack is Uriah Heep: Demons and Wizards.
I'm on to chapter 11 of Basic Math & Pre-Algebra for Dummies, "Dallying with Decimals," which will go over converting fractions to decimals and vice versa, as well as covering the basics of working with decimals in the big four operations.
Fractions and decimals both serve to let us divide something into even portions. Every fraction can be represented as a decimal.
Leading zeros don't change the value of whole numbers (027 = 27); in the same way, trailing zeros don't change the value of a decimal (0.270 = 0.27).
To divide any number by 10, move the decimal point one place to the left; to multiply any number by 10, move the decimal point one point to the right.
To add or subtract numbers with decimals, simply line up the decimals and proceed as normal, carrying the decimal point all the way down.
To multiply numbers with decimals, multiply as if the decimal points weren't there at all, then count how many digits followed the decimal point(s) and include the same number of digits after the decimal point in the answer, including any trailing zeros in the calculation.
To divide a number with a decimal, move the decimal of the divisor all the way to the right, making it a whole number. Move the decimal of the dividend the same number of places to the right. Then put a decimal directly above the decimal of the dividend on the division box. Interestingly, remainders are never allowed in a decimal division. Thus, we must round to the expected place value. To round a decimal to a whole number, add one trailing zero to the dividend; for one decimal place, add two trailing zeros, and so on.
To convert a decimal less than 1 to a fraction, put the number over a 1 followed by the same number of zeros as the number of digits that follow the decimal point, then reduce as needed (.25 = 25/100 = 1/4; .025 = 25/1000 = 1/40).
To convert a decimal greater than 1 to a fraction, complete the same steps, and leave the whole number off to the side, making it a mixed-number fraction.
To convert a fraction to a decimal, divide the numerator by the denominator and perform a decimal division, adding enough trailing zeros to the the numerator to determine whether the answer is a terminating decimal or a repeating decimal. To represent a repeating decimal in an answer, just put a bar on top of the repeating number or number series (not across, but atop - like a little pancake hat).
