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3.07 Decimals in the real world

Lesson

Practical problems with decimal operations

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.

Examples

Example 1

Harry buys an item from the school canteen for \$3.20. If he pays for it with a five dollar note, how much change will he get back?

Worked Solution
Create a strategy

Use the subtraction vertical algorithm to find how much change he will get back.

Apply the idea

Set up the subtraction: \begin{array}{c} & &5 &.&0&0 \\ &- &3&.&2&0 \\ \hline \\ \hline \end{array}

0-0=0 so write a 0 below the last digit. \begin{array}{c} & &5 &.&0&0 \\ &- &3&.&2&0 \\ \hline &&&&&0 \\ \hline \end{array}

0 is less than 2 so we need to borrow from 5, to make it 10-2=8.\begin{array}{c} & &4 &.&{}^1 0&0 \\ &- &3&.&2&0 \\ \hline & & &.&8&0 \\ \hline \end{array}

Find 4-3=1.\begin{array}{c} & &4 &.{}^1 &0&0 \\ &- &3&.&2&0 \\ \hline & & 1&.&8&0 \\ \hline \end{array}

So the change due is \$ 1.80.

Example 2

How many 0.38\text{ L} bottles can be filled from a barrel which holds 41.8\text{ L}?

Worked Solution
Create a strategy

Use short division to find out how many bottles can be filled.

Apply the idea
The image shows the short division of 4180 divided by 38. Ask your teacher for more information.

Set up the division.

The image shows the short division of 4180 divided by 38. Ask your teacher for more information.

38 can't go into 4, so 38 into 41 goes once remainder 3.

So we write 1 above 41 and carry the 3.

The image shows the short division of 4180 divided by 38. Ask your teacher for more information.

38 into 38 goes once, so write a 1 above the 8.

The image shows the short division of 4180 divided by 38. Ask your teacher for more information.

Write a 0 above the 0 at the end of the number.

The result is 110 bottles.

Example 3

At midnight, the temperature in Darwin is 29.6 \degree \text{C}. Each hour after that the temperature decreases by 2.34\degree\text{C} until the sun comes up. What is the temperature 4 hours after midnight?

Worked Solution
Create a strategy

Use multiplication and subtraction vertical algorithm to find the temperature.

Apply the idea

To find how much the temperature decreased by, multiply 2.34 by 4:

Set up the multiplication: \begin{array}{c} & &2 &. &3 &4 \\ &\times & & & &4 \\ \hline \\ \hline \end{array}

Multiply each digit by 4: \begin{array}{c} & & ^12\,\, & . & ^13\,\, & 4\\ & \times & & & & 4\\ \hline & & 9 & . & 3 & 6\\ \hline \end{array}

So the temperature will decrease by 9.36 \degree\text{C} in 4 hours. We need to subtract this from 29.6.

Set up the subtraction:\begin{array}{c} & &2 &9 &. &6 &0 \\ &- &0 &9 &. &3 &6 \\ \hline \\ \hline \end{array}

Subtract each digit from the left, borrowing when necessary:\begin{array}{c} & &2 &9 &. &5 &^{1}0 \\ &- &0 &9 &. &3 &6 \\ \hline & &2 &0 &. &2 &4 \\ \hline \end{array}

So the temperature will be 20.24 \degree\text{C}.

Idea summary

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.

  • What are the quantities that we are combining?

  • What units do we expect the answer to have?

  • What operations will combine the relevant quantities to produce the expected units?

  • What magnitude do we expect the answer to have?

  • Does the answer we calculate seem appropriate in the context?

Outcomes

MA4-5NA

operates with fractions, decimals and percentages

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