ANTMACK215 × WEALTHWISEGUYS
WealthWiseGuys Practical Mathematics

Chapter 3

Decimals

Dollars and cents, gas prices, receipts, and unit pricing

Money is written in decimals. This chapter shows how to read and round decimals, convert them to and from fractions, compute with them on a real receipt, and compare prices with unit pricing.

3.1

Reading, Rounding, and Converting Decimals

Learning objectives

After this section you will be able to:

  1. Name decimal places: tenths, hundredths, thousandths.
  2. Round decimals, including to the nearest cent.
  3. Convert fractions to decimals and decimals to fractions.

Real-life situation

Why gas prices have three decimals

A gas station posts regular at $3.479 per gallon. Your card is charged in cents, so the station rounds the final total to two decimal places.

Regular

$3.479

per gal

Plus

$3.879

per gal

Premium

$4.199

per gal

Figure 3.1 Posted fuel prices (dollars per gallon)

The concept

Places to the right of the decimal point are tenths, hundredths, thousandths, and ten-thousandths. In money, the hundredths place is cents.

Rounding decimals follows the same rule as whole numbers: look one place to the right of the rounding place. Digits after the rounding place are dropped (not replaced with zeros).

A fraction is a division problem: numerator ÷ denominator. To change a decimal to a fraction, write the digits over 10, 100, or 1,000 (one zero per decimal place) and reduce.

Reading, Rounding, and Converting Decimals: solution map

  1. 1

    Identify the question

    Round $3.479 to the nearest cent.

  2. 2

    Calculation 1

    Cents are the hundredths place: 7.

  3. 3

    Calculation 2

    The digit to the right is 9, so round up: 3.48.

  4. 4

    Interpret and check

    $3.48

Figure 3.1.V Reading, Rounding, and Converting Decimals: solution map. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • sales tax

    A percentage added by the government to the price of many purchases.

  • discount

    An amount taken off a regular price.

  • cost

    The amount paid to make or buy an item before it is sold.

Key terms

Decimal point
The dot separating whole units from parts of a unit.
Tenths, hundredths, thousandths
The first, second, and third places right of the decimal point.
Repeating decimal
A decimal whose digits repeat forever, such as 0.666…

Formulas & rules

  • Fraction → decimal

    a/b = a ÷ b

  • Decimal → fraction

    0.65 = 65/100 = 13/20

Worked examples

Example 1Nearest cent

Round $3.479 to the nearest cent.

Solution

  1. 1Cents are the hundredths place: 7.
  2. 2The digit to the right is 9, so round up: 3.48.

Answer: $3.48

Example 2Fraction to decimal

Write 3/8 as a decimal.

Solution

  1. 13 ÷ 8: 8 into 30 is 3 (24, remainder 6); into 60 is 7 (56, remainder 4); into 40 is 5.
  2. 2Result 0.375.

Answer: 0.375

Example 3Decimal to fraction

Write 0.65 as a fraction in lowest terms.

Solution

  1. 1Two decimal places → over 100: 65/100.
  2. 2GCD of 65 and 100 is 5: 13/20.

Answer: 13/20

Practice exercises 3.1

  1. Round 12.3462 to the nearest hundredth.
  2. Write 7/20 as a decimal.
  3. Write 0.125 as a fraction in lowest terms.
  4. Write 2/3 as a decimal rounded to the nearest hundredth.
  5. Write 0.07 in words.

Recap quiz 3.1

1. Round 4.0951 to the nearest tenth.
2. 1/4 as a decimal:
3. Which is largest?

Section 3.1 recap

  • Each decimal place is a power of ten: tenths, hundredths, thousandths.
  • To compare decimals, line up the decimal points and compare place by place.
Answer key with explanations: Section 3.1

Practice exercises

  1. 12.35
  2. 0.35
  3. 1/8
  4. 0.67
  5. Seven hundredths

Recap quiz

  1. 4.1: Tenths digit 0, next digit 9 → round up to 4.1.
  2. 0.25: 1 ÷ 4 = 0.25.
  3. 0.5: Compare tenths first: 5 tenths beats 4 tenths.
3.2

Adding, Subtracting, Multiplying, and Dividing Decimals

Learning objectives

After this section you will be able to:

  1. Add and subtract decimals by lining up decimal points.
  2. Multiply decimals by counting decimal places.
  3. Divide by a decimal by moving the decimal point.

Real-life situation

Back-to-school receipt

Kayla buys school supplies at a store that charges 6% sales tax and pays with $30. She wants to verify the subtotal, tax, total, and change.

Market St. Supply Co.

08/28 · Thank you!

3 × Notebook @ $1.25$3.75
1 × Gel pens (pack) @ $4.99$4.99
1 × Scientific calculator @ $12.50$12.50
SUBTOTAL$21.24
TAX 6%$1.27
TOTAL$22.51
CASH$30.00
CHANGE$7.49
Figure 3.2 School-supply receipt with 6% sales tax

The concept

Adding and subtracting: line up the decimal points, fill empty places with zeros, and work like whole numbers. The decimal point in the answer goes straight down.

Multiplying: multiply as if there were no decimal points, then count the total decimal places in both factors. The product gets that many decimal places.

Dividing: if the divisor is a decimal, move its decimal point right until it is a whole number, and move the dividend's decimal point the same number of places. Then divide normally.

Adding, Subtracting, Multiplying, and Dividing Decimals: solution map

  1. 1

    Identify the question

    Find the subtotal, tax, total, and change from $30.

  2. 2

    Calculation 1

    Notebooks: 3 × 1.25 = 3.75.

  3. 3

    Calculation 2

    Subtotal: 3.75 + 4.99 + 12.50 = 21.24.

  4. 4

    Calculation 3

    Tax: 21.24 × 0.06 = 1.2744 → $1.27.

  5. 5

    Calculation 4

    Total: 21.24 + 1.27 = 22.51.

  6. 6

    Calculation 5

    Change: 30.00 − 22.51 = 7.49.

  7. 7

    Interpret and check

    Subtotal $21.24, tax $1.27, total $22.51, change $7.49

Figure 3.2.V Adding, Subtracting, Multiplying, and Dividing Decimals: solution map. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • selling price

    The price a customer pays for an item or service.

  • revenue

    The total money a business brings in from sales, before any costs are paid.

  • expense

    Money a business spends to run, such as rent, supplies, or wages.

Key terms

Subtotal
Total of items before tax.
Sales tax
A percent of the subtotal added by the state or city.

Formulas & rules

  • Sales tax

    Tax = Subtotal × rate (as a decimal)

  • Total

    Total = Subtotal + Tax

  • Decimal places in a product

    places(a × b) = places(a) + places(b)

Worked examples

Example 1Verifying the receipt

Find the subtotal, tax, total, and change from $30.

Solution

  1. 1Notebooks: 3 × 1.25 = 3.75.
  2. 2Subtotal: 3.75 + 4.99 + 12.50 = 21.24.
  3. 3Tax: 21.24 × 0.06 = 1.2744 → $1.27.
  4. 4Total: 21.24 + 1.27 = 22.51.
  5. 5Change: 30.00 − 22.51 = 7.49.

Answer: Subtotal $21.24, tax $1.27, total $22.51, change $7.49

Example 2Multiplying

4.6 × 0.35

Solution

  1. 146 × 35 = 1,610.
  2. 2Decimal places: 1 + 2 = 3.
  3. 31.610 = 1.61.

Answer: 1.61

Example 3Dividing by a decimal

A $18.75 ride is shared by distance: each unit costs $2.50. How many units? (18.75 ÷ 2.5)

Solution

  1. 1Move both decimals one place: 187.5 ÷ 25.
  2. 225 × 7 = 175; remainder 12.5; 12.5 ÷ 25 = 0.5.
  3. 37.5.

Answer: 7.5

Practice exercises 3.2

  1. 14.6 + 3.75 + 0.08
  2. 50 − 17.86
  3. 2.4 × 1.5
  4. 9.6 ÷ 0.12
  5. A 12-pack of water costs $6.60. What is the price per bottle?

Recap quiz 3.2

1. 0.3 × 0.2 =
2. 5 − 0.25 =
3. 1.2 ÷ 0.4 =

Section 3.2 recap

  • Line up the decimal points to add or subtract decimals.
  • When multiplying, count the total decimal places; when dividing, move the point to make a whole-number divisor.
Answer key with explanations: Section 3.2

Practice exercises

  1. 18.43
  2. 32.14
  3. 3.6
  4. 80
  5. $0.55

Recap quiz

  1. 0.06: 3 × 2 = 6 with two decimal places.
  2. 4.75: 5.00 − 0.25 = 4.75.
  3. 3: 12 ÷ 4 = 3.
3.3

Powers of Ten and Unit Pricing

Learning objectives

After this section you will be able to:

  1. Multiply and divide decimals by 10, 100, and 1,000 mentally.
  2. Compute unit prices.
  3. Choose the better buy.

Real-life situation

Which cereal is the better deal?

Two boxes of the same cereal sit side by side. The bigger box costs more, but is it cheaper per ounce?

Cereal family size

$4.32

18 oz

Cereal regular

$3.12

12 oz

Spicy chips 18-bag box

$12.42

18 × 1 oz

Spicy chips share bag

$2.60

3.25 oz

Figure 3.3 Shelf tags: cereal and snack packs (hypothetical prices)

The concept

Multiplying by 10, 100, or 1,000 moves the decimal point right 1, 2, or 3 places. Dividing moves it left. Add zeros as placeholders when needed.

Unit price is the cost of one unit (one ounce, one pound, one item). It lets you compare different package sizes fairly. Stores often print unit prices on shelf tags; check them.

Powers of Ten and Unit Pricing: solution map

  1. 1

    Identify the question

    3.45 × 100 and 72.5 ÷ 1,000

  2. 2

    Calculation 1

    × 100: move right two places → 345.

  3. 3

    Calculation 2

    ÷ 1,000: move left three places → 0.0725.

  4. 4

    Interpret and check

    345; 0.0725

Figure 3.3.V Powers of Ten and Unit Pricing: solution map. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • balance

    The amount of money in an account at a given moment.

  • invoice

    A document listing goods or services sold and the amount owed.

  • payment terms

    The rules in an agreement about when a bill must be paid and any discounts for paying early.

Key terms

Unit price
Price for one unit of measure.
Better buy
The option with the lower unit price, assuming you will use it all.

Formulas & rules

  • Unit price

    Unit price = Total price ÷ Number of units

  • × 10ⁿ

    Move the decimal n places right

  • ÷ 10ⁿ

    Move the decimal n places left

Worked examples

Example 1Powers of ten

3.45 × 100 and 72.5 ÷ 1,000

Solution

  1. 1× 100: move right two places → 345.
  2. 2÷ 1,000: move left three places → 0.0725.

Answer: 345; 0.0725

Example 2Snack-pack unit pricing

A box of 18 one-ounce bags of rolled spicy chips costs $12.42. A single 3.25 oz share bag costs $2.60 (hypothetical prices). Which costs less per ounce?

Solution

  1. 1Box: 18 bags × 1 oz = 18 oz. 12.42 ÷ 18 = 0.69 → $0.69/oz.
  2. 2Share bag: 2.60 ÷ 3.25 = 0.80 → $0.80/oz.
  3. 30.69 < 0.80, so the box is cheaper per ounce — if you will actually eat 18 bags before they go stale.

Answer: The 18-bag box, $0.69/oz vs $0.80/oz

Example 3Cereal comparison

Which box has the lower price per ounce?

Solution

  1. 1Family: 4.32 ÷ 18 = 0.24 → $0.24/oz.
  2. 2Regular: 3.12 ÷ 12 = 0.26 → $0.26/oz.
  3. 30.24 < 0.26.

Answer: The 18 oz family size is the better buy

Practice exercises 3.3

  1. 0.062 × 1,000
  2. 485 ÷ 100
  3. An 8 lb bag of rice costs $11.92. What is the price per pound?
  4. Which is the better buy: 6 juice boxes for $4.50 or 10 for $7.20?
  5. Printing costs $0.035 per flyer. What do 1,000 flyers cost?

Recap quiz 3.3

1. 5.6 ÷ 10 =
2. A 24 oz bottle costs $6.00. Unit price:
3. 0.9 × 100 =

Section 3.3 recap

  • Multiplying by a power of ten moves the decimal point one place per zero.
  • Unit price = total price ÷ quantity — the fair way to compare package sizes.
Answer key with explanations: Section 3.3

Practice exercises

  1. 62
  2. 4.85
  3. $1.49
  4. 6 for $0.75 each vs 10 for $0.72 each → the 10-pack
  5. $35

Recap quiz

  1. 0.56: Move the decimal one place left.
  2. $0.25/oz: 6 ÷ 24 = 0.25.
  3. 90: Move the decimal two places right.
3.4

Decimals and Percents in Online Shopping

Learning objectives

After this section you will be able to:

  1. Convert between percents and decimals.
  2. Find a sale price from a percent-off tag.
  3. Compute an online cart total with a promo code and sales tax.

Real-life situation

Checkout time

Maya fills an online cart with earbuds, two phone cases, and a charging cable. A promo code takes 20% off the cart, and 6% sales tax is added at checkout. Before she taps "Place order" she wants to know what she will really pay. The store and prices are hypothetical.

Your cart (4 items)

Wireless earbuds × 1$79.99
Phone case × 2$29.00
USB-C charging cable × 1$9.99
Subtotal$118.98
Promo 20% off−$23.80
Est. tax 6%$5.71
Order total$100.89

Hypothetical store and prices.

Figure 3.4 Online shopping cart with promo code (hypothetical)

The concept

Percent means "per hundred." To change a percent to a decimal, drop the % sign and move the decimal point two places left: 20% = 0.20, 6% = 0.06, 7.5% = 0.075.

A percent-off sale removes that percent of the original price. You can find the discount and subtract, or multiply by what is left: 25% off means you pay 75%, or 0.75 of the price.

At checkout, stores usually apply the promo code first and then charge sales tax on the discounted amount. Round money to the nearest cent at each step shown on the receipt.

Fleece hoodie

$60.00

25% OFF

Now $45.00

Figure 3.5 Sale tag on a hoodie (hypothetical)

Decimals and Percents in Online Shopping: solution map

  1. 1

    Identify the question

    A $60.00 hoodie is 25% off. What is the sale price?

  2. 2

    Calculation 1

    25% = 0.25.

  3. 3

    Calculation 2

    Discount: 60.00 × 0.25 = 15.00.

  4. 4

    Calculation 3

    Sale price: 60.00 − 15.00 = 45.00.

  5. 5

    Calculation 4

    Shortcut check: 60.00 × 0.75 = 45.00. ✓

  6. 6

    Interpret and check

    $45.00

Figure 3.4.V Decimals and Percents in Online Shopping: solution map. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • checking account

    A bank account for everyday spending, usually with a debit card and checks.

  • deposit

    Money placed into a bank account.

  • withdrawal

    Money taken out of a bank account.

Key terms

Percent
A ratio out of 100.
Discount
The dollar amount taken off a price.
Sale price
Original price minus discount.
Promo code
A code that applies a discount to an online order.

Formulas & rules

  • Percent → decimal

    p% = p ÷ 100

  • Discount

    Discount = Price × Rate

  • Sale price

    Sale price = Price × (1 − Rate)

  • Cart total

    Total = (Subtotal − Discount) × (1 + Tax rate)

Worked examples

Example 1The sale tag

A $60.00 hoodie is 25% off. What is the sale price?

Solution

  1. 125% = 0.25.
  2. 2Discount: 60.00 × 0.25 = 15.00.
  3. 3Sale price: 60.00 − 15.00 = 45.00.
  4. 4Shortcut check: 60.00 × 0.75 = 45.00. ✓

Answer: $45.00

Example 2Maya's cart

Find the order total in Figure 3.4.

Solution

  1. 1Subtotal: 79.99 + 2 × 14.50 + 9.99 = 79.99 + 29.00 + 9.99 = 118.98.
  2. 2Promo: 118.98 × 0.20 = 23.796 → $23.80.
  3. 3After discount: 118.98 − 23.80 = 95.18.
  4. 4Tax: 95.18 × 0.06 = 5.7108 → $5.71.
  5. 5Total: 95.18 + 5.71 = 100.89.

Answer: $100.89

Practice exercises 3.4

  1. Write 8.5% as a decimal.
  2. Sneakers priced $120.00 are 15% off. Find the sale price.
  3. A $49.99 game is 40% off. Find the discount, rounded to the nearest cent.
  4. Cart subtotal $64.00, promo 10% off, then 6% tax. Find the total.
  5. Which is cheaper: $35 off a $140 jacket, or 30% off the same jacket?

Recap quiz 3.4

1. 6% as a decimal is:
2. 25% off $80 leaves a price of:
3. At checkout, sales tax is usually charged on:

Section 3.4 recap

  • A percent discount comes off the price; sales tax is added on top of the discounted amount.
  • Work in steps: subtotal → discount → taxed amount → total.
Answer key with explanations: Section 3.4

Practice exercises

  1. 0.085
  2. 120 × 0.85 = $102.00
  3. 49.99 × 0.40 = 19.996 → $20.00
  4. 64 − 6.40 = 57.60; tax 3.456 → 3.46; total $61.06
  5. $35 off → $105; 30% off → $98. The 30% deal is cheaper

Recap quiz

  1. 0.06: Move the decimal two places left.
  2. $60: 80 × 0.75 = 60.
  3. The discounted amount: The promo comes off first; tax applies to what you actually pay for the items.

Chapter 3 Organizer and Review

Chapter Organizer

Every section at a glance: key formulas, key terms, and the main idea.

  • 3.1 Reading, Rounding, and Converting Decimals

    Key formulas

    • Fraction → decimal: a/b = a ÷ b
    • Decimal → fraction: 0.65 = 65/100 = 13/20

    Key terms

    Decimal point, Tenths, hundredths, thousandths, Repeating decimal

    Remember

    Each decimal place is a power of ten: tenths, hundredths, thousandths.

  • 3.2 Adding, Subtracting, Multiplying, and Dividing Decimals

    Key formulas

    • Sales tax: Tax = Subtotal × rate (as a decimal)
    • Total: Total = Subtotal + Tax
    • Decimal places in a product: places(a × b) = places(a) + places(b)

    Key terms

    Subtotal, Sales tax

    Remember

    Line up the decimal points to add or subtract decimals.

  • 3.3 Powers of Ten and Unit Pricing

    Key formulas

    • Unit price: Unit price = Total price ÷ Number of units
    • × 10ⁿ: Move the decimal n places right
    • ÷ 10ⁿ: Move the decimal n places left

    Key terms

    Unit price, Better buy

    Remember

    Multiplying by a power of ten moves the decimal point one place per zero.

  • 3.4 Decimals and Percents in Online Shopping

    Key formulas

    • Percent → decimal: p% = p ÷ 100
    • Discount: Discount = Price × Rate
    • Sale price: Sale price = Price × (1 − Rate)
    • Cart total: Total = (Subtotal − Discount) × (1 + Tax rate)

    Key terms

    Percent, Discount, Sale price, Promo code

    Remember

    A percent discount comes off the price; sales tax is added on top of the discounted amount.

Cumulative Review

Mixed practice from this chapter and the two chapters before it.

  1. Section 3.1

    Write 0.07 in words.

    Show answer

    Seven hundredths

  2. Section 3.2

    A 12-pack of water costs $6.60. What is the price per bottle?

    Show answer

    $0.55

  3. Section 3.3

    Printing costs $0.035 per flyer. What do 1,000 flyers cost?

    Show answer

    $35

  4. Section 3.4

    Which is cheaper: $35 off a $140 jacket, or 30% off the same jacket?

    Show answer

    $35 off → $105; 30% off → $98. The 30% deal is cheaper

  5. Review of Section 1.3

    125 × 48

    Show answer

    6,000

  6. Review of Section 2.3

    2/3 × 9/10

    Show answer

    18/30 = 3/5

All prices, stores, people, and accounts in this chapter are hypothetical and for teaching only. Product references are generic categories; no brand endorses or is endorsed by this textbook.

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