I Cents Are Hundredths of a Dollar

Cents Are Hundredths of a Dollar

One dollar is $100$ cents: one cent is therefore one hundredth of a dollar. $$1\text{ cent}=\dfrac{1}{100}\text{ dollar}=\dollar 0.01$$ The decimal point of a price is the decimal point of the decimal numbers: a price written with a decimal point is a decimal number of dollars. $$\dollar 3.45=3\text{ dollars and }45\text{ cents}=3+\dfrac{45}{100}\text{ dollars}$$

Dollars	.	Tenths ($10$ cents)	Hundredths ($1$ cent)
	.
$3$	.	$4$	$5$

On a price label, a price is usually written with two digits after the point: the digits before the point count the dollars, and the two digits after the point count the cents, that is the hundredths of a dollar.
The first digit after the point counts the tenths of a dollar: one tenth of a dollar is $10$ cents, the value of a $10$-cent coin. In $\dollar 3.45$, the $4$ tenths are $40$ cents and the $5$ hundredths are $5$ cents: $\dollar 3.45=3+\dfrac{4}{10}+\dfrac{5}{100}$ dollars.
As a decimal number, the same price can also be written with one digit after the point: $\dollar 2.5=\dollar 2.50$, because $5$ tenths are $50$ hundredths. It is $2$ dollars and $50$ cents, not $2$ dollars and $5$ cents.

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Definition — Coins and Bills

1 dollar
2 dollars
5 dollars
10 dollars
20 dollars

1 cent $= \dollar 0.01$
5 cents $= \dollar 0.05$
10 cents $= \dollar 0.10$
25 cents $= \dollar 0.25$
50 cents $= \dollar 0.50$

Skills to practice

Calculating the Total in Decimal Form
Checking If You Have Enough Money to Buy Items
Reading a Price in Tenths and Hundredths of a Dollar

II Giving Change from a Bill

Method — Counting Up to the Next Dollar

To give change when the price has cents and the customer pays with bills or dollar coins, the seller counts up from the price:

To the next dollar: add the cents that are missing to make $100$.
Then in dollars: add dollars until the money given is reached.
The change is the cents and the dollars counted on the way.

Skills to practice

Giving Change from a Bill

III Rounding a Cash Total to the Nearest 5 Cents

Rounding a Cash Total to the Nearest 5 Cents

In some countries, there are no 1-cent or 2-cent coins: the coin with the smallest value is the $5$-cent coin. There, a total paid in cash is rounded to the nearest 5 cents, because a total that does not end in $0$ or $5$ cents could not be paid exactly with the coins. A total paid by card is not rounded.
This is a rule of those countries, not a general rule for money: it is used only where there are no $1$-cent or $2$-cent coins.
Only the last digit of the cents is looked at:

Total	$\dollar 7.41$, $\dollar 7.42$	$\dollar 7.43$, $\dollar 7.44$	$\dollar 7.46$, $\dollar 7.47$	$\dollar 7.48$, $\dollar 7.49$
Last digit	$1$ or $2$	$3$ or $4$	$6$ or $7$	$8$ or $9$
Cash total	$\dollar 7.40$ (down)	$\dollar 7.45$ (up)	$\dollar 7.45$ (down)	$\dollar 7.50$ (up)

A total that ends in $0$ or in $5$, such as $\dollar 7.40$ or $\dollar 7.45$, stays as it is. Going up can reach the next dollar: $\dollar 7.98$ and $\dollar 7.99$ become $\dollar 8.00$.
For example, a total of $\dollar 7.44$ paid in cash with a $\dollar 10$ bill: the cash total is $\dollar 7.45$, and the change is $\dollar 10 - \dollar 7.45 = \dollar 2.55$.

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Skills to practice

Rounding a Cash Total

IV Solving Money Problems

Method — Choosing the Operation in a Price Problem

Together, in all, the total $\rightarrow$ an addition.
How much more, how much less, what is left $\rightarrow$ a subtraction.
The same article several times $\rightarrow$ a multiplication.
The double is twice the price; the half is the price shared in two.
Two steps: sometimes the answer needs an intermediate number that the statement does not give — the price of the three notebooks, the total of two purchases. That number is computed first, and only then the question is answered.

The words are a clue, not a rule: what decides is what the question asks.

Skills to practice

Solving Money Problems

V Review & Quizz

Skills to practice

Quiz

Dollars	.	Tenths (\(10\) cents)	Hundredths (\(1\) cent)
	.
\(3\)	.	\(4\)	\(5\)

1 cent \(= \dollar 0.01\)
5 cents \(= \dollar 0.05\)
10 cents \(= \dollar 0.10\)
25 cents \(= \dollar 0.25\)
50 cents \(= \dollar 0.50\)

Total	\(\dollar 7.41\), \(\dollar 7.42\)	\(\dollar 7.43\), \(\dollar 7.44\)	\(\dollar 7.46\), \(\dollar 7.47\)	\(\dollar 7.48\), \(\dollar 7.49\)
Last digit	\(1\) or \(2\)	\(3\) or \(4\)	\(6\) or \(7\)	\(8\) or \(9\)
Cash total	\(\dollar 7.40\) (down)	\(\dollar 7.45\) (up)	\(\dollar 7.45\) (down)	\(\dollar 7.50\) (up)