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Ch 2: Conversions & Budgeting·§2.0 Chapter overview
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Chapter 2

Conversions & Budgeting

Percent, unit conversions, and building a budget you could actually use — anchored by the first Major Assignment.

This week is about three moves that show up in adult life everywhere: percent, conversions, and budgeting. By Sunday you'll compute tip and tax in your head, convert any unit to any other unit, and have a real budget you could plug your own numbers into.

The math is mostly arithmetic. What you're really learning is how to set things up — in your head, on paper, and in Excel — so the math works for you.

By the end of this chapter, you'll be able to…

  • 2.1Solve application problems involving percent.
  • 2.2Convert units using dimensional analysis.
  • 2.3Convert between fractions, decimals, and percentages.
  • 2.4Use budgeting techniques to help develop financial literacy skills.

Sections

  1. 2.1What is a percent, really?Percent is just a fancy way of saying "out of 100." Once that clicks, every percent problem becomes the same simple recipe.Read →
  2. 2.2Three masks, one number.Fractions, decimals, and percents are three ways to write the same number. Once you can switch between them on demand, you can pick the form that makes the math easiest.Read →
  3. 2.3Percent in the wild.Tip, sales tax, raises, discounts, markup. Different stories, same recipe. This lesson teaches you the move and the one-step shortcut that pays off all term.Read →
  4. 2.4Multiply by 1, in disguise.Every unit conversion uses the same elegant move: multiply by a fraction equal to 1, written so the unwanted unit cancels. Once you see it, you can convert anything.Read →
  5. 2.5Chain the move.When one factor isn't enough, stack several. Each one cancels a unit until what's left matches your target. Same recipe as Lesson 4, scaled up.Read →
  6. 2.6Tell your money what to do.A budget is a math instrument. It tells your dollars where to go before they vanish. Once you set it up in a spreadsheet, the percent and conversion tricks from this whole topic do the heavy lifting.Read →
Start with §2.1 →

Chapter summary

Formulas, key concepts, and the kind of one-page reference you'd want during a problem set.

This chapter is the foundation for everything financial in the rest of the book. By the end of these six sections you can move fluently between fractions, decimals, and percents; apply percent to tip, tax, discount, and percent change; convert any unit to any other unit using dimensional analysis; and build a budget that holds together as numbers change. The math is mostly arithmetic; the real skill is recognizing which recipe a problem is asking for.

Chapter glossary

All key terms introduced across this chapter, in the order they appear in the reading.

Percent
A fraction whose denominator is 100. The % symbol means "divide by 100."
Base
The whole, the 100% reference. In "$60, 25% off," the base is $60.
Part
The piece you're computing or comparing to the base. In the same example, the part (the discount amount) is $15.
Decimal form
A percent rewritten without the % sign. 25% = 0.25. Always shift the decimal two places to the left.
Fraction
A ratio: top over bottom (numerator over denominator). 1/4 means 1 part out of 4 equal parts.
Decimal
Place value to the right of the decimal point: tenths, hundredths, thousandths. 0.25 means two tenths plus five hundredths.
Conversion
The move you make to rewrite a number from one form to another. The recipes: fraction to decimal = divide top by bottom; decimal to percent = multiply by 100; percent to decimal = divide by 100.
Markup
An increase added to a base price. A store buys an item for $20, marks it up 50%, and sells it for $30.
Discount
A decrease taken off a base price. A $60 sweater on sale at 30% off costs $42.
Tip
A percent added to a restaurant bill, usually 15%-20% in the U.S. Math is the same as sales tax.
Sales tax
A percent added to a purchase price by the state or city. Rates vary, often between 5% and 9%.
Percent change
The catch-all term for any move that increases or decreases a base by a percent. ALEKS uses this language often.
Conversion factor
A fraction whose numerator and denominator are equivalent quantities in different units, e.g. 5280 ft / 1 mi or 2.54 cm / 1 in. Always equals 1.
Dimensional analysis
The formal name for this technique. Set up a chain of conversion factors so the original unit cancels and the target unit survives.
Numerator / Denominator
Top of the fraction / bottom of the fraction. Which slot a unit lives in determines whether it cancels or survives.
Equivalent quantities
Two measurements that name the same physical amount: 12 inches and 1 foot, 1000 grams and 1 kilogram, 4 quarts and 1 gallon.
Chain
Two or more conversion factors multiplied in a row. Cancellation propagates link by link until the surviving unit matches the target.
Compound unit
A unit that's a ratio of two units: mph (miles/hour), $/gal (dollars/gallon), kg/L (kilograms/liter). Convert the top and the bottom separately.
Currency conversion
Just unit conversion with money. The exchange rate IS the conversion factor. 1 USD = 0.92 EUR means the factor is 0.92 EUR / 1 USD.
Income
Money coming in: paycheck, side hustle, gifts. Use take-home pay (after tax) for budgeting, not gross.
Expenses
Money going out, broken into categories. Rent, food, transport, subscriptions, discretionary spending. Each category is a line item.
Fixed vs. variable
Fixed expenses are the same every month (rent, phone bill, insurance). Variable expenses change (groceries, gas, eating out).
Savings rate
Savings as a percent of income. savings / income × 100%. Higher is better. 10-20% is solid for an early-career budget.
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