Exercises: Operations with decimal numbers

Michael is saving up to buy a video game. On Monday he had $\$24,50$ in his piggy bank. On Tuesday his aunt gave him $\$15,75$ and on Wednesday he decided to buy a phone case that cost him $\$12,30$. How much money does Michael have in his piggy bank right now? Perform the operation by correctly aligning the decimal points.

In Technology class, Ashley is measuring various components for a robotics project. She has placed four identical pieces in a row, as shown in the illustration. If each piece is $3,25$ inches long, what is the total length of the row?

A monthly subscription to a music platform costs $\$9,95$. 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 shifting the decimal point to the right.

In the school cafeteria, a large bag of nuts costs $\$3,45$. Three friends decide to buy it to share and pay equally. How much money must each one contribute? Perform the division making sure to obtain exactly two decimal places.

Work out the following products and divisions by powers of 10 mentally. Remember that you only have to shift the decimal point to the left or right as appropriate:

1. a) $45,8 \cdot 100 =$
2. b) $125,3 : 10 =$
3. c) $0,75 \cdot 1000 =$
4. d) $34,2 : 100 =$

Apply the order of operations to solve the following expression with decimal numbers. Remember to perform the operation inside the parentheses first:

A can of soda has a capacity of $0,33$ gallons. If a cardboard box holds 12 cans, how many gallons of soda are there in total in a full box? Perform the multiplication manually.

Emma wants to put a square rug in her bedroom. If the area occupied by the rug is $5,29$ sq ft, how long is the side of the rug? Calculate the exact square root of the decimal number. (Hint: Think about 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:

$15,8 - 2,5 \cdot (4,2 - 3,75) + (1,24 + 0,36) : 0,4$

A streamer is analyzing the data usage of their latest live streams. In the first hour they consumed $2,45$ GB, in the second hour $1,8$ GB and in the third, due to a technical failure, only $0,95$ GB. If they have a monthly plan of $15$ GB and had already spent $6,25$ GB before starting these live streams, how many gigabytes do they have left available in their plan?

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

An architect is designing a rectangular play area in a local park. The dimensions of the land are $12,45$ feet long by $8,6$ feet wide. If she wants to surround the entire perimeter with a protective fence that costs $\$15,75$ per linear foot, what will be the total budget for the fence?

In a swimming competition, the times of the top three finishers in the $100$-yard 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 medal winner and the bronze medal winner. What is the mean time of the three swimmers? Round the result of the mean to two decimal places.

A grocer buys $50$ pounds of bulk cherries for a total of $\$142,50$. Upon checking the goods, he detects that $4,5$ pounds are damaged and cannot be sold. If he wants to obtain a net profit of $\$60$ on the total purchase, at what price must he sell the pound of cherries that are in good condition?

A water tank has a capacity of $120,5$ gallons. A faucet is opened that pours $4,25$ gallons per minute. Simultaneously, the tank has a leak through which $0,75$ gallons per minute are lost. If the tank initially contained $15,25$ gallons, how many gallons will it have accumulated after $12$ minutes of operation?

Emma has $\$154,20$ in her bank account. During the week she carries out the following operations:

• Pays an internet bill of $\$32,45$.

• Receives a Venmo transfer from her grandmother of $\$20,50$.

• Buys three identical books for a total of $\$41,85$.

• Withdraws $\$50$ from the ATM for the weekend.

If the bank charges her a maintenance fee of $\$2,15$ at the end of the week, what is her final balance? Has she gone into the red (negative balance)? Write the result using integers and decimals.

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

• Subscription to a gaming channel: $\$12,45$.

• Snack with friends: $\$8,12$.

• Phone case: $\$5,67$.

• Sticker pack: $\$1,23$.

Calculate the value of the following expression to find how much money you have left in your bank account if you initially had $\$150$ and, in addition to the purchases, the bank has charged you a maintenance fee of $\$2,25$:

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

The new logo of 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 decals. The radius of the larger circle measures $6,25$ in and the radius of the inner circle is $3,5$ in.

Using $\pi \approx 3,1416$ as the value, calculate the area of the shaded zone by performing the operations with all the decimals and round the final result to two decimal places.

A racing drone has traveled a distance of $14,58$ miles in a time of $12$ minutes and $45$ seconds.

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

2. Calculate the average speed of the drone in mph using the previous data.

3. If the circuit record is a speed of $70,25$ mph, how many miles per hour was the drone short of equaling the record?

In a bulk nut shop, they want to prepare a special "Energy" mix. They mix $2,5$ pounds of walnuts at $\$14,20$/lb, $1,75$ pounds of almonds at $\$12,60$/lb and $0,75$ pounds of raisins at $\$6,45$/lb.

Due to handling, it is estimated that the total weight of the mixture is reduced by $0,05$ pounds due to the loss of shells and dust. At what price must they sell a pound of the resulting mixture to obtain a total profit of $\$15,50$ over the cost of the ingredients?

An architect designs a swimming pool in the shape of a rectangular prism whose internal measurements are $5,25$ ft long, $3,40$ ft wide and $1,85$ ft deep.

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

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

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

A hummingbird's heart beats approximately $1,2 \cdot 10^3$ times per minute at rest.

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

2. If the average life expectancy of this hummingbird is $5,5$ years, how many beats will it make in total throughout its life? (Consider that a year has $365,25$ days).

3. If one beat displaces $0,025$ fluid ounces of blood, how many gallons of blood does it pump in an 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:

You have bought components to build a gaming computer in an online store. The initial budget was the following:

• Graphics card: $\$450,95$.

• Processor: $\$215,50$.

• RAM memory: $\$89,99$.

The shop applies a promotional discount of $5,5\%$ on the total purchase before taxes. After applying the discount, $21\%$ sales tax must be added. What is the total amount of the invoice? Perform all calculations with two decimal places (rounding at each intermediate step).