Dollars before the point, cents after it
$3.45 is 3 whole dollars and 45 cents. The decimal point splits the amount in two: the dollars are in front of it, and the cents come after it.
Three $1 bills and 45 cents in coins make $3.45.
A cent is a hundredth of a dollar
A dollar is 100 cents, so one cent is one hundredth of a dollar. Think of a dollar as a square cut into 100 small squares, one for each cent. 45 cents fill 45 of the 100 squares: 45 hundredths of a dollar. As a decimal, 45 hundredths is written 0.45, so 45 cents is $0.45.
That is why money is written with two places after the point. The first place counts tenths of a dollar, which are ten-cent amounts, and the second counts hundredths, which are single cents. In $0.45 the 4 stands for 4 tenths, which is 40 cents, and the 5 stands for 5 hundredths, which is 5 cents.
45 of the 100 squares are shaded: 45 hundredths of a dollar, which is $0.45.
Cents to dollars, and back
To change dollars to cents, multiply by 100, because each dollar is 100 cents. $3.45 is 3 × 100 + 45 = 345 cents.
To change cents to dollars, divide by 100. Dividing by 100 moves every digit two places to the right, so 345 cents is $3.45, and 45 cents is $0.45.
× 1 moves no digit, so the value is unchanged
Turn 45 into 0.45
Dividing by 100 moves the 4 and the 5 two places to the right, past the decimal point: 45 cents is $0.45.
Same digits, different money
$3.45 and $3.54 use the same digits, but they are different amounts. The dollars are equal, so compare the cents, starting from the left. $3.54 has 5 tenths of a dollar and $3.45 has only 4, so $3.54 is more: 54 cents against 45 cents, which is 9 cents more.
The 45 bright squares are 45 cents, and the 9 dimmer squares after them take it on to 54 cents: 54 cents is 9 cents more.
A hundred cents make the next dollar
Adding cents can make a whole dollar. $3.45 plus 55 cents adds 45 + 55 = 100 cents, which is one more dollar, so the total is $4.00.
Two places, not one
A dollar is 100 cents, not 10, so cents change to dollars by dividing by 100. Dividing 345 cents by 10 gives $34.50, which is ten times too much: 345 cents is $3.45.
The digits after the point are only part of the amount. $3.45 is not 45 cents: the 3 dollars in front of the point are another 300 cents, so $3.45 is 345 cents.
Worked example: Prices in Cents and Dollars with Change from a Note
Question Mr Lee buys 6 pens at 85 cents each and 4 files at $2.40 each. He pays with a $20 note. (a) How much do the pens and files cost altogether? (b) How much change does he receive?
1.Write the price of a pen in dollars: 85 cents = $0.85. The 6 pens cost 6 × 0.85 = $5.10.
In dollars a pen costs $0.85, so the 6 pens cost 6 × 0.85 = $5.10. 2.The 4 files cost 4 × 2.40 = $9.60.
The 4 files cost 4 × 2.40 = $9.60. 3.(a) The total cost is 5.10 + 9.60 = $14.70.
(a) Altogether they cost 5.10 + 9.60 = $14.70. 4.(b) The change from the note is 20 − 14.70 = $5.30. Check: 14.70 + 5.30 = 20.
(b) The change from the $20 note is 20 − 14.70 = $5.30.
Answer: (a) $14.70; (b) $5.30
Common mistakes
- Working out 6 × 85 + 4 × 2.40 = 519.60. The 85 is a number of cents and the 2.40 is a number of dollars, so one of them must be converted before they are added.
- Writing 85 cents as $8.50 or $0.085. One cent is one hundredth of a dollar, so 85 cents is $0.85.