# Dimensional Analysis With Scientific Notation

l>Quiz of the Week

## Quiz of the Week - Chemistry 221 Dimensional Analysis and Scientific Notation

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### A Quick Recheck out of Dimensional Analysis

Dimensionalanalysis,also recognized as the factor-label method,is a problem resolving technique utilizing units (labels) and conversion components. Units tell us the form of measurementbeing made; for example, "5.2 cm" has a unit (cm) which tells us themeasurement to be made is size. Conversionfactors (additionally well-known as "equalities") are fractions that relatetwo kinds of units; for instance, "6.0 cm / s" tells us that for every1 second that passes (time), 6.0 cm are covered (length). Notice that "6.0cm s-1" is the same as "6.0 cm / s" in unit notation.

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Most difficulties ask a question whose answer isa number through its unit. Problems additionally provide information that containsnumbers through their systems. Multiply the indevelopment by conversion components sothat all units cancel other than the devices necessary in the answer. (A unit in the numerator might be canceled byplacing the very same unit in the denominator of the bordering conversion element.Conversely, a unit in the denominator may be canceled by placing the exact same unitin the numerator of the surrounding convariation variable.)

Numbers and devices are considered individually.Multiply by as many convariation determinants as crucial.Typical conversion components might or may not be provided with the problem.

Examples:

1. How many kind of hours are in 6 days?

2. How many seconds are in 5 hours?

3. How many type of feet per second is 5 miles per hour?

A common variation occurs once more than one piece of information is provided through the trouble. In these situations, begin with the information that includes the sametype of devices as the answer. (For example, if size systems are essential inthe numerator of the answer, use the indevelopment that consists of size devices andararray it so that those length units are in the numerator.) Next, multiply byconvariation components so that undesirable systems cancel.

Test Yourself:

1. How many type of gallons of milk does a household drink in 5days if they drink 4 pints per day? Answer: 2.5 gallons

2. How many minutes will certainly it take an automobiletraveling 60 miles per hour to take a trip a distance of 400 miles? Answer: 400 minutes

### A Fast Resee of Scientific Notation

Scientific Notation is supplied by researchers to express very large and exceptionally little numbers in a compact fashion.

To express a number in clinical notation, we rewrite the quantity as a number(between 1 and 10) times 10 raised to a power (exponent) that tells us exactly how wemoved the decimal point.

Multiply the number by 100 (100 = 1)Move the decimal suggest to offer a numberin between 1 and 10Eextremely time we shift the decimal suggest tothe left by one area, we boost the value of the exponent by oneEexceptionally time we transition the decimal point tothe right by one place, we minimize the value of the exponent by oneExample: Write 120,000 in scientific notation.120,000= 120,000 x 100 = 1.2 x105

Example: Write 0.0000012 in clinical notation.

0.0000012 = 0.0000012 * 100 = 1.2 x 10-6

To expush a number that is composed in scientific notation as a non-exponential quantity:

Move the decimal point the same number of places as the value of the exponent and eliminate the exponentialcomponent of the number.If the exponent is positive, we move the decimal to the ideal to the same number of places as the value of the exponent. The result must be a number greater than 1 unless the originalnumber is negative.If the exponent is negative, we relocate the decimal to the left to the exact same number of locations as the value of theexponent. The outcome must be a number much less than 1 unless the original number is negative.

Example: Write 1.23 * 106 in non-exponential form.

1.23 x 106 = 1,230,000

Example: Write 1.11 * 10-5 in non-exponential form.