Exercises: Operations with decimal numbers

In a cell phone accessory store, Mateo wants to buy a case costing $249$ pesos and a screen protector costing $178$ pesos. If Mateo pays with a $1\,000$ pesos bill, how much change will he receive at the register?

Work out these calculations mentally using powers of ten. Remember to move the decimal point to the correct side depending on whether you multiply or divide:

1. a) $34.57 \times 10$
2. b) $0.23 \times 100$
3. c) $458.2 : 10$
4. d) $12.5 : 1000$

Marta went to the greengrocer's and bought $2.5$ kg of apples at $1.80$ pesos per kilogram. On arriving home, she notices that one of the apples is bad and decides to return it. If the apple weighed $0.25$ kg, how much money should Marta be refunded?

To make a recipe, we need to divide a $1.5$ kg bag of flour into $6$ equal portions to make muffins. How many kilograms of flour will each portion weigh? Express your answer in grams as well.

Work out the following combined operations, respecting the order of operations (brackets, multiplications/divisions, and finally additions/subtractions):

1. a) $4.5 + 2.1 \times 3$
2. b) $(12.8 - 3.4) : 2$
3. c) $5 \times 0.25 + 1.75$

A group of $4$ friends goes to the cinema. The total for tickets and popcorn came to $45.80$ pesos. If they decide to split the cost equally, how much money must each person pay? If one of them only has a $10$ pesos note and a $2$ pesos coin, will they have enough money?

Copy and complete the following statements by writing the missing decimal number to make each calculation correct:

1. a) $15.45 + \dots = 20$
2. b) $7.2 - \dots = 4.55$
3. c) $\dots \times 3 = 12.9$

An athlete is training on a circular track. Each lap of the track is $0.45$ km long. If today she completed a total of $12$ laps, how many kilometers did she cover in total? If her goal was to run $6.3$ km, how many more laps should she have completed?

Three friends decide to have an afternoon snack together. They buy a pack of soft drinks for $97$ pesos, a family-size bag of chips for $46$ pesos and a box of small cakes for $109$ pesos. If they pay with a $400$ pesos bill, how much money will they have left over to buy candy afterwards?

A spool of filament for a 3D printer weighs exactly $1.25$ kg. If $0.015$ kg of plastic is used to make a small part, how many complete parts can be made from a single spool? How much filament will be left over at the end?

Valentina wants to download three video game files on her console. The first file is $4.35$ GB, the second is double the first, and the third is $1.2$ GB less than the second. If her connection downloads at a constant speed of $0.05$ GB per second, how many seconds will it take to complete the download of all three files?

Calculate the result of the following combined operations, respecting the order of operations:

1. a) $12.5 + 3.8 \times (6.4 - 2.15)$

1. b) $(15.4 + 8.6) : 2.5 - 1.02 \times 4$

A municipality wants to fence a rectangular park measuring $25.4$ meters long and $12.75$ meters wide. The price of the fence is $304$ pesos per meter. If the total available budget is $24\,000$ pesos, do they have enough money to enclose the entire park? Justify your answer with the necessary calculations.

In a "Back to School" offer, a pack of $5$ notebooks costs $165$ pesos, whereas if you buy them individually, each one costs $36$ pesos.

What is the total saving if we decide to buy $15$ notebooks using the pack offer instead of buying them separately?

A marathon runner has completed a stage of $15.6$ km in an hour and a half ($1.5$ hours).

1. a) What was their average speed in km/h?
2. b) If they maintain the same speed, how many kilometers will they cover in $2.25$ hours?

A courier service charges a fixed fee of $4.50$ pesos per delivery, plus $0.85$ pesos for each kilogram of the parcel's weight. If we want to send a parcel weighing $3.4$ kg and apply a discount voucher of $1.25$ pesos to the final price, how much will the delivery cost? Write a single numerical expression for the calculation and solve it.

Calculate the result of the following mixed operation, strictly respecting the order of operations and working with all decimal places obtained:

Once the final result is obtained, approximate it by rounding to the nearest hundredth and by truncating to the nearest tenth.

In an electronics store, a video game costs $\$59.95$. During "Black Friday" week, they offer a discount of a quarter of its value. If a teenager decides to buy it and hands over a $\$50$ bill, calculate:

1. a) The final price of the video game after applying the discount (round to the nearest pesos cent if necessary).
2. b) Will they have enough money? If they are short, state how much. If they have money left over, state the exact change they will receive.

A farmer has a water tank with a total capacity of $1\,250,5$ liters. Due to a small crack, the tank loses $0.75$ liters every hour. At the same time, a water pump pours $12.4$ liters into the tank every $15$ minutes. If the tank currently contains $840.25$ liters:

How many liters will be in the tank after exactly $4$ hours and a half? Express the result to two decimal places.

Look at the rectangle in the figure, with base $b = 12.45 \text{ cm}$ and height $h = 8.2 \text{ cm}$.

Calculate its area and its perimeter. Then, imagine that we reduce both the base and the height to half. What will the new area be? Is the resulting area half of the original or has it changed in some other way? Justify your answer by carrying out the necessary operations.

Three friends want to buy a subscription to a streaming platform that costs $\$17.99$ per month. They decide to split the cost as follows: Juan will pay half, Marta will pay one third of the remainder, and Lucía will pay whatever is left.

Calculate the exact amount (with all its decimal places) that each person must contribute. If the bank only allows payment to two decimal places, who do you think should absorb the rounding of the extra cent so that the sum is exactly $\$17.99$?

A Formula 1 car took $1 \text{ minute}$ and $24.352 \text{ seconds}$ to complete one lap of the circuit. If its main rival took $84.12 \text{ seconds}$ to cover the same distance:

1. a) Which of the two was faster?
2. b) Calculate the time difference between them expressed in seconds.
3. c) If the first car maintains its pace, how long will it take to complete $15$ full laps? Express the result in minutes and seconds.

We are cooking a recipe that requires $0.250 \text{ kg}$ of flour to make $6$ muffins. If we want to invite the whole class ($28$ students) and we want each of them to eat $2$ muffins:

1. a) How much flour will we need in total? Express the result in kilograms.
2. b) If we buy flour packets of $0.75 \text{ kg}$, how many packets will we need to buy at least? How much flour will we have left over exactly?

Alex's cell phone plan has a fixed monthly fee of $\$22.50$. If he exceeds the included gigabytes, each extra GB costs $\$0.50$, and each minute of international calls costs $\$0.12$. This month he has made $45$ minutes of international calls and the cost of the extra GB was exactly one fifth of the fixed fee:

1. a) How many extra GB has he used?
2. b) What is the total bill before tax?
3. c) If $21\%$ tax must be added to the total (multiply by $0.21$ and add to the total), what will be the final price of the bill? (Round the final result to the nearest pesos cent).