A hundred cents is a dollar
Count four 25¢ coins: 25, 50, 75, 100. Together they are worth exactly 100 cents, and 100 cents is one dollar.
Other coins make a dollar too. Ten 10¢ coins count 10, 20, 30, 40, 50, 60, 70, 80, 90, 100: that is also 100 cents, so it is also one dollar.
Four 25¢ coins count 25, 50, 75, 100: one dollar.
Ten 10¢ coins count up to 100 as well: one dollar.
One bill for a hundred cents
Those 100 cents can be traded for one dollar bill. The bill is worth the same as the coins, and it is much easier to carry.
The sign $ means dollars, and it is written in front of the number. So $1 is one dollar, and $1 = 100 cents.
A $1 bill is worth the same as 100 cents.
Bills and coins together
Bills count dollars and coins count cents, so count them in two parts. Three $1 bills are 3 dollars. A 25¢ coin and a 10¢ coin are 25 + 10 = 35 cents. Together that is 3 dollars and 35 cents.
It is written $3.35. The dollars come before the dot, and the cents come after it. The dot is called the decimal point.
Three $1 bills and 35 cents in coins: 3 dollars and 35 cents, written $3.35.
Two places for the cents
The cents always take two digits after the decimal point. 4 dollars and 5 cents is written $4.05: the 0 keeps the 5 in the cents. $4.50 is 4 dollars and 50 cents, a different amount.
Three and a half dollars is 3 dollars and 50 cents, so it is written $3.50. The 0 at the end stays, because the cents take two places.
Dollars are not cents
A bill is not a cent. Three $1 bills and 35 cents are not 38 cents: each bill is 100 cents by itself.
The other way round, 240 cents is not $240. Take out each 100 cents as one dollar: 240 cents is 2 dollars and 40 cents, which is $2.40.
Worked example: A Jar of Ten-Cent Coins in Dollars and Cents
Question Ben empties his jar. It has 24 ten-cent coins in it. (a) How much money is in the jar? Give the answer in dollars and cents. (b) Ben wants to have $3. How many more ten-cent coins does he need?
1.Put the coins in rows of 10. Ten 10-cent coins are 100 cents, and 100 cents is $1.
A full row is ten 10-cent coins. That is 100 cents, which is $1. 2.24 coins make 2 full rows and 4 more coins. That is $2 and 4 × 10 = 40 cents.
There are 2 full rows and 4 more coins: $2 and 40 cents. 3.(a) There are 240 cents in the jar, which is $2.40.
(a) 240 cents is $2.40. 4.$3 is 300 cents. Count up from 240 in tens: 250, 260, 270, 280, 290, 300. That is 6 tens.
Count up in tens from 240 to 300. Each new coin is 10 cents. 5.(b) Ben needs 6 more ten-cent coins. Check: 4 + 6 = 10 coins fill the third row.
(b) Ben needs 6 more coins. They fill the third row.
Answer: (a) $2.40; (b) 6 coins
Common mistakes
- Writing 24 coins as 24 cents. Each coin is worth 10 cents, so the coins are counted in tens, and 24 tens are 240 cents.
- Writing 240 cents as $240. One dollar is 100 cents, so 240 cents is 2 dollars and 40 cents, which is $2.40.
Worked example: The Same Amount Saved Every Day
Question Siti puts a 50-cent coin into her money box every day. (a) How much money does she save in 7 days? (b) She wants to buy a book that costs $4.50. How many days does she need to save for it altogether?
1.Two 50-cent coins make 100 cents, which is $1. So every 2 days Siti saves $1.
Two 50-cent coins make $1. Siti saves $1 every 2 days. 2.Count on one day at a time: 50 cents, $1, $1.50, $2, $2.50, $3, $3.50.
The total after each day is under the coin. 3.(a) In 7 days Siti saves $3.50.
(a) In 7 days Siti saves $3.50. 4.Keep counting until the total reaches $4.50. Day 8 makes $4 and day 9 makes $4.50.
Day 8 makes $4 and day 9 makes $4.50. 5.(b) Siti needs 9 days altogether.
(b) Siti needs 9 days altogether.
Answer: (a) $3.50; (b) 9 days
Common mistakes
- Writing 7 × 50 = 350 and giving the answer as $350. The 350 is in cents, and 350 cents is $3.50.
- Answering 2 days for part (b). Two more days are needed after the first 7, but the question asks for all the days: 7 + 2 = 9.