3.025 Convert rates | Year 11 Maths | Australian Curriculum 11 Essential Mathematics - 2020 Edition (2024)
Convert rates
Convertingrates allows us to compare rates given in different unitsand to also obtain a rate in unit suitable for a particular application.
To convert a rate, we want to multiply or divide the rate by the appropriate constant. So to convert a rate in m/min to m/s, we want to divide the rate by$60$60. This is because a rate given in m/min, tells us the number of metres per minute, which is the number of metres per$60$60seconds.
Worked examples
Example 1
Convert the rate of $20$20L/hto a rate in L/min.
Think: We first need to identify which unitwe are changing. Is it the first unit, the second unit or are we converting both? In this case, we are only changing time from hours to minutes. We also need to identify what the conversion factor between these units is.In our case, $1$1 hour is equivalent to $60$60 minutes.
Do: The number of litres in an hour must be$60$60times more than the number of litres in a minute. So we want to divide the given rate by$60$60.
Rate
$=$=
$20$20L/h
Write the rate as a division including units.
$=$=
$\frac{20}{60}$2060L/min
Convert hours to minutes by dividing by $60$60.
$=$=
$\frac{1}{3}$13L/min
Simplify the fraction if possible.
Example 2
How fast is Usain Bolt's world record speed of $12.2$12.2m/sin km/h?
Think: Both the distance unit and time unit are being converted. Let's first change the distance unit.In this case, we arechanging distance from metres to kilometres. The number of metres travelled in a given second is$1000$1000times greater than the number of kilometres, so we want to divide the rate by$1000$1000.
Then we want to convert the new rate in km/s to km/h. There are$60$60seconds in a minute, and then$60$60minutes in an hour, so the number of kilometres travelled in an hour will be the rate in km/s multiplied by$60^2$602.
Do:
Rate
$=$=
$12.2$12.2m/s
Write the rate as a fraction including units.
$=$=
$12.2/1000$12.2/1000km/s
Convert metres to kilometres by dividing by $1000$1000.
$=$=
$0.0122$0.0122km/s
Simplify the rate.
$=$=
$0.0122\times60^2$0.0122×602km/h
Convert seconds to hours by multiplying by$60^2$602.
$=$=
$43.92$43.92km/h
Simplify the rate.
Reflect:Alternatively, we can convert km/s to km/h by converting in stages. First we can find the rate in km/m, by multiplying by$60$60and then we can find the rate in km/h by multiplying by$60$60again.
Careful!
When converting units think carefully about if your answer should get smaller or larger and, if you need to divide or multiply by the conversion factor. For instance, the distance you travel in metres in an hour, should be greater than the number of kilometres travelled in an hour. So a rate in m/h should be greater if it was given in km/h.
To convert a rate, we want to multiply or divide the rate by the appropriate constant. So to convert a rate in m/min to m/s, we want to divide the rate by $$60. This is because a rate given in m/min, tells us the number of metres per minute, which is the number of metres per $$60 seconds.
Equivalent rates can be used to compare different sets of quantities that have the same value. A rate that compares a quantity to one is called a unit rate. The unit rate has a denominator equal to one when written as a fraction. Unit rates can be used to find larger equivalent rates.
Conversion rates are calculated by simply taking the number of conversions and dividing that by the number of total ad interactions that can be tracked to a conversion during the same time period. For example, if you had 50 conversions from 1,000 interactions, your conversion rate would be 5%, since 50 ÷ 1,000 = 5%.
You can write any rate as a unit rate by reducing the fraction so it has a 1 as the denominator or second term. As a unit rate example, you can show that the unit rate of 120 students for every 3 buses is 40 students per bus. You could also find the unit rate by dividing the first term of the ratio by the second term.
How do you calculate rate in math? Rate is defined as the change in one unit divided by the change in a second unit. For example, to find the rate of change in miles per hour, divide the number of miles traveled by the amount of time traveled.
The difference between the two rates R2-R1 with its 95% Confidence Interval and associated P-value. If the P-value is less than 0.05 it can be concluded that there is a statistical significant difference between the two rates.
A rate is anything that can be gained or lost over time. There are two ways you can write this mathematically. You can write it using division like so - rate = gain or loss/time - or, you can write it using multiplication like this - gain or loss = rate * time.
Step 1: First write the ratio a:b in the form of fraction a/b. Step 2: Multiply the fraction a/b by 100 to convert in terms of percentage. Step 3: Finally, add the percentage symbol (%) to the resultant value.
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