Exercises: Operations with decimal numbers

Marcos is saving up to buy a video game. On Monday he had $1\,470$ pesos in his piggy bank. On Tuesday his aunt gave him $945$ pesos and on Wednesday he decided to buy a phone case costing $738$ pesos. How much money does Marcos have in his piggy bank right now? Perform the calculation lining up the decimal points correctly.

In Design and Technology class, Sara is measuring several components for a robotics project. She has placed four identical pieces in a row, as shown in the diagram. If each piece measures $3.25$ cm long, what is the total length of the row?

A monthly subscription to a music streaming service costs $9.95$ pesos. If a group of 10 friends decides to create a family account that costs exactly 10 times that amount per year, what will be the total annual cost of the family subscription? Solve by moving the decimal point to the right.

In the school canteen, a large bag of mixed nuts costs $3.45$ pesos. Three friends decide to buy it to share and split the cost equally. How much money should each person contribute? Perform the division making sure you get two exact decimal places.

Calculate the following products and quotients by powers of 10 mentally. Remember that you only need to move the decimal point to the left or right as appropriate:

1. a) $45.8 \times 100 =$
2. b) $125.3 : 10 =$
3. c) $0.75 \times 1000 =$
4. d) $34.2 : 100 =$

Apply the order of operations to solve the following expression with decimal numbers. Remember to carry out the operation inside brackets first:

A can of fizzy drink has a capacity of $0.33$ liters. If a cardboard box holds 12 cans, how many liters of drink are there in total in a full box? Work out the multiplication manually.

Ainhoa wants to put a square rug in her room. If the area covered by the rug is $5.29$ m², what is the length of the side of the rug? Calculate the exact square root of the decimal number. (Hint: Think which integer multiplied by itself gives $529$).

Calculate the result of the following expression according to the order of operations and the rule of signs:

$15.8 - 2.5 \times (4.2 - 3.75) + (1.24 + 0.36) : 0.4$

A streamer is analysing the data consumption of their recent live streams. In the first hour they used $2.45$ GB, in the second hour $1.8$ GB, and in the third, due to a technical glitch, only $0.95$ GB. If they have a monthly plan of $15$ GB and had already spent $6.25$ GB before starting these streams, how many gigabytes do they have left in their data plan?

Complete the gaps in the pyramid so that the value of each box is the sum of the two numbers directly below it.

An architect is designing a rectangular play area in a local park. The dimensions of the ground are $12.45$ meters long by $8.6$ meters wide. If she wants to enclose the entire perimeter with a protective fence costing $15.75$ pesos per linear meter, what will be the total budget for the fence?

In a swimming competition, the times of the top three swimmers in the $100$-meter freestyle event were:

• Swimmer A: $48.25$ seconds.

• Swimmer B: $49.12$ seconds.

• Swimmer C: $48.09$ seconds.

Calculate the time difference between the gold medalist and the bronze medalist. What is the mean time of the three swimmers? Round the mean to two decimal places.

A greengrocer buys $50$ kg of loose cherries for a total of $8\,550$ pesos. When inspecting the goods, he discovers that $4.5$ kg are damaged and cannot be sold. If he wants to make a net profit of $3\,600$ pesos on the total purchase, at what price per kilogram must he sell the cherries that are in good condition?

A water tank has a capacity of $120.5$ liters. A faucet is turned on that pours in $4.25$ liters per minute. Simultaneously, the tank has a leak through which $0.75$ liters per minute are lost. If the tank initially contained $15.25$ liters, how many liters will it have after $12$ minutes of operation?

Marta has $9\,252$ pesos in her bank account. During the week she carries out the following transactions:

• Pays an internet bill of $1\,947$ pesos.

• Receives a cell phone transfer from her grandmother of $1\,230$ pesos.

• Buys three identical books for a total of $2\,511$ pesos.

• Withdraws $3\,000$ pesos from an ATM to spend over the weekend.

If the bank charges her a maintenance fee of $129$ pesos at the end of the week, what is her final balance? Is her account overdrawn (negative balance)? Write the result using integers and decimals.

An automatic savings app rounds each of your purchases up to the nearest pesos and saves the difference in a digital piggy bank. During an afternoon of shopping, you made the following payments:

• Subscription to a gaming channel: $12.45$ pesos.

• Afternoon snack with friends: $8.12$ pesos.

• Phone case: $5.67$ pesos.

• Sticker pack: $1.23$ pesos.

Calculate the value of the following expression to find how much money you have left in your bank account if you initially had $150$ pesos and, in addition to the purchases, the bank charged you a maintenance fee of $2.25$ pesos:

Where $H$ is the total sum of the roundings sent to the digital piggy bank.

The new logo for an e-sports team consists of an annulus (the shaded area between two concentric circles). The designer needs to know the exact area to order the vinyl stickers. The radius of the larger circle measures $6.25$ cm and the radius of the inner circle is $3.5$ cm.

Using as the value of $\pi \approx 3.1416$, calculate the area of the shaded region working with all decimals during the calculations, and round the final result to two decimal places.

A racing drone has traveled a distance of $14.58$ kilometers in $12$ minutes and $45$ seconds.

1. Express the total flight time in hours using decimal numbers (round to four decimal places).

2. Calculate the average speed of the drone in km/h using the previous value.

3. If the circuit record is a speed of $70.25$ km/h, by how many kilometers per hour did the drone fall short of matching the record?

In a bulk dried fruit and nut shop, they want to prepare a special "Energy" mix. They mix $2.5$ kg of walnuts at $852$ pesos/kg, $1.75$ kg of almonds at $756$ pesos/kg, and $0.75$ kg of raisins at $387$ pesos/kg.

Due to handling, it is estimated that the total weight of the mix is reduced by $0.05$ kg due to the loss of shells and dust. At what price per kilogram should they sell the resulting mix to obtain a total profit of $930$ pesos over the cost of the ingredients?

An architect designs a swimming pool in the shape of a cuboid whose internal dimensions are $5.25$ m long, $3.40$ m wide and $1.85$ m deep.

1. Calculate the maximum volume of water the pool can hold in cubic meters.

2. If the architect estimates the volume by truncating each dimension to one decimal place, what is the estimated volume?

3. Calculate the absolute error made between the actual volume and the volume estimated by truncation.

A hummingbird's heart beats approximately $1.2 \times 10^3$ times per minute at rest.

1. How many times does its heart beat in a full day? Express the result in scientific notation.

2. If the average life expectancy of this hummingbird is $5.5$ years, how many beats will it make in total throughout its life? (Assume a year has $365.25$ days).

3. If one beat displaces $0.025$ milliliters of blood, how many liters of blood does it pump in one hour?

Solve the following combined operation respecting the order of operations and working with generating fractions when recurring numbers appear. Express the final result in decimal form rounded to three decimal places: