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4.04 Percentages with technology

Lesson

Introduction

When working with larger or more complex numbers it can become tiresome to evaluate everything by hand and it is for this reason that we have digital technologies that can do this part for us. When using a calculator to solve percentage and decimal problems, there are a few buttons on the calculator that we will need to know about.

Percentages and decimals on a calculator

When inputting decimals into a calculator we use the "." button. Using this button, we can input decimals by pressing this button after the ones digit and before the tenths digit. To input 15.9 into our calculator we press:

The calculator buttons for 1, 5, decimal point and  9.

To get the calculator to return the answer of 15.9 we should also press the = or the "enter" button.

Depending on the type of calculator, the result of a calculation will be expressed as either a decimal or as a fraction.

A calculator button with the letters S and D on it, with a two way arrow between the letters.

To convert from a fraction to a decimal we can use this button.

When converting percentage values into non-percentage values without a calculator, we would remove the \% symbol and then divide by 100. This method doesn't change when using a calculator, we just don't have to evaluate the division by ourselves.

There are also some calculators that have a percentage function which may be stored as an alternative command. On most calculators, this function has the same effect as dividing by 100.

If the calculator's \% function acts as division by 100 then the output of will be the decimal or fraction equivalent to the percentage inputted. We can use this function to convert percentage values into non-percentage values by inputting them into the calculator and evaluating the expression.

It should be noted that the calculator cannot give percentage values as outputs. In our working out we would usually multiply by 100\% to convert a non-percentage value into a percentage value. When using a calculator we need to break this up into two steps:

  1. Multiply the non-percentage value by 100

  2. Attach the \% symbol to the result when writing the answer

To input 59\% into the calculator, we press:

The calculator buttons for 5 9 and  percentage.

To get the calculator to return the value we should also press the = or the "enter" button.

If the calculator's \% function acts as division by 100 then the output of this expression will be 0.59 or \dfrac{59}{100}.

Examples

Example 1

Lisa scored 70\% on her Maths exam, which was actually out of 140. What was Lisa's actual mark out of 140?

Worked Solution
Create a strategy

Multiply the total marks by the percentage.

Apply the idea
\displaystyle \text{Mark}\displaystyle =\displaystyle 70\% \times 140Multiply the percentage by the total marks
\displaystyle =\displaystyle 98Evaluate using the percent button on the calculator
Idea summary
A calculator button with the letters S and D on it, with a two way arrow between the letters.

To convert from a fraction to a decimal we can use this button.

To input 15.9 into our calculator we press:

The calculator buttons for 1, 5, decimal point and  9.

To input 59\% into the calculator, we press:

The calculator buttons for 5 9 and  percentage.

Followed by the = or \text{enter}.

Outcomes

VCMNA248

Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies

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