A student writes 9 cents as $0.9 on a price tag. What is wrong with this notation?
ANothing — $0.9 correctly represents 9 cents
B$0.9 means 9 dimes (90 cents), not 9 pennies — it should be written $0.09
CThe dollar sign should not be used for amounts less than one dollar
D9 cents should be written as $9.00
The two digits after the decimal point represent tens-of-cents (dimes) and ones-of-cents (pennies). $0.9 places the 9 in the dimes column, making it 90 cents. To write 9 pennies with no dimes, a 0 is needed in the dimes slot: $0.09. This leading zero is essential — the cents part always fills two positions.
Question 2 Multiple Choice
A store sells two items: one for $1.30 and another for $1.03. How much more does the first cost than the second?
ANothing — they cost the same because both contain the digits 1, 3, and 0
B$0.27, because 30 cents minus 3 cents equals 27 cents
C3 cents, because the tens-of-cents digits differ by 3
DThey cannot be compared without more information
$1.30 = 1 dollar and 30 cents. $1.03 = 1 dollar and 3 cents. The difference is 27 cents ($0.27). In $1.30 the 3 sits in the dimes column (30 cents); in $1.03 the 3 sits in the pennies column (3 cents). Position determines value — the same digit is worth ten times more in the dimes slot than in the pennies slot.
Question 3 True / False
The decimal point in dollar amounts like $4.75 separates the dollars (left) from the cents (right).
TTrue
FFalse
Answer: True
The decimal point is the boundary between whole dollars and parts of a dollar (cents). Everything to its left counts full dollars; everything to its right counts cents out of 100. This is why dollar notation previews decimal place value: just as 4.75 means 4 wholes and 75 hundredths, $4.75 means 4 dollars and 75 cents.
Question 4 True / False
$0.7 and $0.07 represent the same amount of money because they both use the digit 7.
TTrue
FFalse
Answer: False
$0.7 means 7 dimes = 70 cents. $0.07 means 7 pennies = 7 cents. They differ by 63 cents. The position of the digit relative to the decimal point determines its value — 7 in the dimes position is worth ten times more than 7 in the pennies position. This is the same place-value principle that makes 70 and 7 different in whole numbers.
Question 5 Short Answer
Why must the cents part of a dollar amount always be written with two digits — for example, $3.07 instead of $3.7 for three dollars and seven cents?
Think about your answer, then reveal below.
Model answer: Because the two digits after the decimal point represent dimes (tens of cents) and pennies (ones of cents). Writing $3.7 puts 7 in the dimes column, meaning 70 cents. To show 7 pennies with no dimes, a 0 must fill the dimes slot: $3.07. The two-digit slot keeps both positional columns correctly filled.
Just as 70 and 7 are different in whole numbers (7 tens vs. 7 ones), the two digits after the decimal point each carry a specific place value. Without the placeholder 0 in the dimes column, the digit shifts to the wrong position and represents ten times more money than intended.