Once we are comfortable performing operations with decimals, we can think about how to manipulate decimal quantities that we come across in the real world. Exchanging money, measuring lengths and weights, and recording times are all areas that make use of decimal numbers.
Lucy is a transport truck driver and pulls into a gas station that advertises unleaded gas for $134.8$134.8 cents per gallon. She fills up her truck with $41.57$41.57 gallons of gas and picks up a $\$5.95$$5.95 bottle of engine oil before paying the cashier. How much will Lucy have to pay? Give your answer in dollars, to the nearest cent.
Think: We know the cost of gas in cents per gallon, and the amount of gas in gallons that Lucy gets. We also know the cost in dollars of the engine oil. Our goal is to combine these quantities to get the total cost in dollars.
Do: A single gallon of gas costs $134.8$134.8 cents, which is $\frac{134.8}{100}=\$1.348$134.8100=$1.348. So the cost in dollars for $41.57$41.57 gallons will be given by the product $1.348\times41.57$1.348×41.57.
Next, we can add the cost of the engine oil, and round the total to two decimal places. The working out for this calculation is shown below.
$\text{Total cost }$Total cost  $=$=  $\text{gas price }\times\text{gas purchased }+\text{engine oil price }$gas price ×gas purchased +engine oil price 

$=$=  $\frac{134.8}{100}\times41.57+5.95$134.8100×41.57+5.95 
Substitute the given information 

$=$=  $1.348\times41.57+5.95$1.348×41.57+5.95 
Simplify the fraction 

$=$=  $56.03636+5.95$56.03636+5.95 
Evaluate the multiplication 

$=$=  $61.98636$61.98636 
Evaluate the addition 

$=$=  $61.99$61.99 
Round to the nearest cent 
The total cost for the gas and the engine oil is $\$61.98636$$61.98636, which is $\$61.99$$61.99 when rounded to the nearest cent.
Reflect: Instead of converting the price of gas to dollars per gallon, we could have found the total cost in cents and converted to dollars at the end. Since we are working in cents rather than dollars, we will round to the nearest whole number rather than to two decimal places. The working out for this method is shown below.
$\text{Total cost }$Total cost  $=$=  $\text{gas price }\times\text{gas purchased }+\text{engine oil price }$gas price ×gas purchased +engine oil price 

$=$=  $134.8\times41.57+5.95\times100$134.8×41.57+5.95×100 
Both quantities are in cents 

$=$=  $5603.636+595$5603.636+595 
Evaluate each multiplication separately 

$=$=  $6198.636$6198.636 
Evaluate the addition 

$=$=  $6199$6199 
Round to the nearest whole number 
Our total cost is $6199$6199 cents, which is the same as $\$61.99$$61.99, as expected.
The solution to many real world problems will eventually involve some kind of calculation, but there is a lot we can do before and after this calculation that can make us more confident our answer is correct.
Harry buys an item from the school canteen for $\$3.20$$3.20. If he pays for it with a five dollar note, how much change will he get back?
How many $0.38$0.38 L bottles can be filled from a barrel which holds $41.8$41.8 L?
At midnight in Alaska, the temperature in Juneau is $36.8$36.8 degrees Fahrenheit.
Each hour after that the temperature decreases by $2.43$2.43 degrees until the sun comes up.
What is the temperature $2$2 hours after midnight?
Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation.