Lesson 8 of 8 · Grades 4 to 5
Decimals and money
Money is where most people meet decimals first. Dollars and cents form a decimal system: the point separates whole dollars from cents, and there are always two places. This lesson puts decimals to work on prices, totals and change.
Dollars and cents
Money is where decimals feel at home. A price such as $3.75 is three whole dollars and seventy-five cents. The decimal point separates the dollars on the left from the cents on the right. One hundred cents make a dollar, so 75 cents is 0.75 of a dollar, or 75 hundredths.
Always two places
Prices always show two places after the point, one for the tens of cents and one for the single cents. Five dollars is written $5.00, not $5. One dollar and fifty cents is written $1.50, not $1.5, even though 1.5 and 1.50 name the same amount. Seven dollars and five cents is $7.05: the tenths place holds a 0 and the hundredths place holds the 5. The zero is what keeps the 5 in the cents place.
Comparing prices
To compare two prices, write both with two decimal places and compare the dollars first, then the tenths, then the hundredths. The prices $4.50 and $4.05 both have 4 dollars. The tenths digits are 5 and 0, so $4.50 is more than $4.05 by 45 cents. The same method shows that 99 cents ($0.99) is less than $1.01.
Totals and change
To find the total cost of several items, add the prices with the decimal points lined up, just as in the last lesson. To find the change, subtract the total from the amount you paid with. If a book costs $6.45 and a pen costs $1.80, the total is $8.25. Paying with a $10 note leaves $1.75 in change, because $10.00 - $8.25 = $1.75.
A useful check when you hand over money: the change plus the total should add back to the amount you paid. $8.25 + $1.75 = $10.00, so the change is correct.
Watch out for this
A short price is a trap. The price $2.5 means two dollars and fifty cents, so it should be written $2.50. It does not mean two dollars and five cents, which is $2.05. When you read a price, count the digits after the point: one digit needs a zero added, and two digits are complete.
Worked example
A book costs $6.45 and a pen costs $1.80. You pay with a $10 note. Work out the total cost and the change.
Step 1: line up the prices by their decimal points: $6.45 and $1.80.
Step 2: add place by place: 5 + 0 = 5 cents, 4 + 8 = 12 tenths, so write 2 and carry 1, then 6 + 1 + 1 = 8 dollars. The total is $8.25.
Step 3: subtract the total from $10.00. Write $10.00 as ten dollars and zero cents.
Step 4: $10.00 - $8.25 = $1.75. Check by adding back: $8.25 + $1.75 = $10.00.
Answer: The total is $8.25 and the change is $1.75.
Remember
- The point separates dollars from cents.
- Prices always show two decimal places: $5 is $5.00.
- Compare dollars first, then tenths, then hundredths.
- Change is the amount paid minus the total.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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How many cents are in $0.85?
Show answer
85 cents. The digits after the point count the cents.
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Write $4.5 with two decimal places.
Show answer
$4.50. Prices always show two places, one for dimes and one for cents.
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Which price is more: $3.09 or $3.9?
Show answer
$3.90. Write it as $3.90 and compare the tenths: 9 is more than 0.
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A juice costs $2.45 and a muffin costs $3.30. What is the total?
Show answer
$5.75. $2.45 + $3.30 = $5.75.
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You pay for a $4.25 sandwich with $5.00. How much change do you get?
Show answer
$0.75. $5.00 - $4.25 = $0.75, which is 75 cents.
Puzzle · Shopping trip
Puzzle time
A book costs $6.45 and a pen costs $1.80. You pay with a $10 note. How much change do you get?
Show a hint
Add the two prices, then take the total away from $10.00.
Show the answer
Answer: $1.75. $6.45 + $1.80 = $8.25, and $10.00 - $8.25 = $1.75.