Recurring Decimal
Recurring Decimal - Related Videos
03:34
Uncertainty in Measurement: Significant Figures
0 Views •
2020
All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values. A measurement result is properly reported when its significant digits accurately represent the certainty of the measurement process. Below are a set of rules to determine the...
07:56
Utilizing Time-Resolved Protein-Induced Fluorescence Enhancement to Identify Stable Local Conformations One α-Synuclein Monomer at a Time
0 Views •
Cited by 5 •
2021
Time-resolved single-molecule protein-induced fluorescence enhancement is a useful fluorescence spectroscopic proximity sensor sensitive to local structural changes in proteins. Here we show it can be used to uncover stable local conformations in α-Synuclein, which is otherwise known as globularly unstructured and unstable when measured using the longer range FRET ruler.
04:34
Scientific Measurement and Lab Skills - Concepts
0 Views •
2020
Two-Dimensional Graphs Some chemistry experiments take the form of directly changing one property of the system that you are studying otherwise known as the independent variable, like temperature, and measuring the effects on another property, otherwise known as the dependent variable, like volume. Once the data have been collected, the interaction between the two parameters must be quantified — or converted into a form that can be evaluated — and compared to other relationships.
08:22
Using Deuterium Oxide as a Non-Invasive, Non-Lethal Tool for Assessing Body Composition and Water Consumption in Mammals
0 Views •
2020
This article describes the deuterium oxide dilution technique in two mammals, an insectivore and carnivore, to determine total body water, lean body mass, body fat mass, and water consumption.
08:12
Experimental Methods to Study Human Postural Control
0 Views •
Cited by 25 •
2019
This article presents an experimental/analytic framework to study human postural control. The protocol provides step-by-step procedures for performing standing experiments, measuring body kinematics and kinetics signals, and analyzing the results to provide insight into the mechanisms underlying human postural control.
FAQs
During long division, a remainder determines the next quotient digit. If a remainder reappears, the same sequence of subsequent digits must follow, because division has returned to an identical state. The possible remainders are limited by the divisor, so a repeated remainder signals a cycle rather than an accidental pattern.
A vinculum, the horizontal bar over a digit or digit block, identifies exactly which decimal places repeat. It separates the recurring portion from any nonrepeating digits before it, making the notation unambiguous. This matters when reading, comparing, or converting the decimal, because only the marked block is repeated indefinitely.
A recurring pattern is evidence that the value belongs to the rational-number framework described by a fraction. By contrast, an irrational number has a decimal representation that does not settle into a repeating block. Inspecting the decimal pattern therefore helps classify a value and prevents treating an exact rational representation as though it were an approximation.
Set the decimal equal to a variable, then multiply by a power of ten that shifts the repeating block into alignment with its original position. Subtracting the two equations cancels the repeated tails, leaving an equation that can be solved for the variable. This method produces a fraction exactly, rather than relying on a rounded decimal.
Each repetition can be treated as a place-value contribution, and the full decimal can be written as a geometric series whose terms continue through the repeated block. Summing that series gives an exact fractional value. This approach is useful when the repeating structure is easier to express as successive place-value terms than through the subtraction step used in algebra.
Carry out long division while recording each remainder. If a remainder repeats, compare the quotient digits produced after the first occurrence with the later sequence, then mark the repeating block with a vinculum. This workflow connects the observed cycle to the exact decimal notation and shows when the calculation should stop instead of continuing indefinitely.
Converting a fraction to a recurring decimal, or reversing that conversion, provides a cross-check between two exact forms of the same value. The decimal form can make numerical comparison convenient, while the fractional form can confirm that no rounding has entered the calculation. These paired representations are especially useful for checking arithmetic and interpreting results in mathematics.