Converting Between Rates
Learn to convert rates for NSW Year 12 Mathematics Standard 1 (NESA outcome MST-12-S1-05). Converting a rate changes its units but not its real size — 72 km/h and 20 m/s describe exactly the same speed.
You will convert the top unit and the bottom unit one step at a time, change km/h to m/s and back, switch flow rates between L/h and mL/min, and rewrite prices and fuel rates in new units — useful for comparing speeds, setting a drip or a garden tap, and reading price labels.
Theory
Converting a rate changes its units but not how fast or how much it really is. This Year 12 Standard 1 (NSW) guide shows how to convert one unit at a time, change km/h to m/s (divide by \(3.6\)) and back, and convert flow rates, prices and fuel rates.
Converting a rate rewrites it in different units without changing its real size. Convert the top unit and the bottom unit one at a time, then check by converting back.
For speed, \(1\text{ m/s}=3600\text{ m}\) per hour \(=3.6\text{ km/h}\). So km/h \(\div 3.6\) gives m/s, and m/s \(\times 3.6\) gives km/h. For flow, mL/min \(\times 60\) gives mL/h, then \(\div 1000\) gives L/h.
For prices, \(\$\) per gram \(\times 1000\) gives \(\$\) per kg, and \(\$\) per kg \(\div 10\) gives \(\$\) per \(100\text{ g}\). For fuel, a car using \(r\) L/100 km travels \(100\div r\) km on \(1\) litre, and a car that travels \(k\) km/L uses \(100\div k\) L/100 km. This is a core Year 12 Standard 1 (NSW) Ratios and rates skill.
Speed conversions use \(1\text{ m/s} = 3.6\text{ km/h}\):
Flow rates, one unit at a time:
Fuel: kilometres per litre from L/100 km:
And back again, L/100 km from km per litre:
How to convert a rate
- Write the rate with both units showing (for example \(400\text{ mL}\) per \(1\text{ min}\)).
- Convert the top unit (amount), multiplying or dividing by the right factor.
- Convert the bottom unit (time or quantity). For speed, use the shortcut \(\div 3.6\) or \(\times 3.6\).
- Check by converting back, and that the size makes sense.
To change km/h into m/s, divide by \(3.6\).
| \(\text{m/s}\) | \(=\) | \(63 \div 3.6\) |
| \(\) | \(=\) | \(17.5\) |
| \(\text{check: } 17.5 \times 3.6\) | \(=\) | \(63\text{ km/h}\) |
The speed is \(17.5\text{ m/s}\).
Multiply by \(3.6\); then distance \(=\) speed \(\times\) time.
| \(\text{(i) km/h}\) | \(=\) | \(12 \times 3.6 = 43.2\) |
| \(\text{(ii) distance}\) | \(=\) | \(12 \times 6\) |
| \(\therefore\ \text{distance}\) | \(=\) | \(72\text{ m}\) |
(i) \(43.2\text{ km/h}\); (ii) \(72\text{ m}\).
Change one unit at a time.
| \(\text{(i) mL/h}\) | \(=\) | \(400 \times 60 = 24\,000\) |
| \(\text{L/h}\) | \(=\) | \(24\,000 \div 1000 = 24\) |
| \(\text{(ii) mL/h}\) | \(=\) | \(4.8 \times 1000 = 4800\) |
| \(\text{mL/min}\) | \(=\) | \(4800 \div 60 = 80\) |
(i) \(24\text{ L/h}\); (ii) \(80\text{ mL/min}\).
Use \(1\text{ kg}=1000\text{ g}\); \(100\text{ g}\) is one tenth of a kilogram.
| \(\text{(i) } 0.025 \times 1000\) | \(=\) | \(\$25\text{ per kg}\) |
| \(\text{(ii) } 18 \div 10\) | \(=\) | \(\$1.80\text{ per 100 g}\) |
| \(\text{(iii) } 100 \div 6.25\) | \(=\) | \(16\text{ km/L}\) |
(i) \(\$25\) per kg; (ii) \(\$1.80\) per \(100\text{ g}\); (iii) \(16\text{ km}\) on \(1\) litre.
Common pitfalls
Frequently asked questions
How do you convert km/h to m/s?
Divide by 3.6. One metre per second is 3600 metres per hour, which is 3.6 km/h. For example 63 km/h divided by 3.6 is 17.5 m/s.
How do you convert m/s to km/h?
Multiply by 3.6. For example 12 m/s times 3.6 is 43.2 km/h.
Why do you divide by 3.6 to change km/h to m/s?
There are 1000 metres in a kilometre and 3600 seconds in an hour. Changing km/h to m/s multiplies by 1000 and divides by 3600, which is the same as dividing by 3.6.
How do you convert mL per minute to litres per hour?
Multiply by 60 to change minutes to hours, then divide by 1000 to change millilitres to litres. For example 400 mL/min is 24 000 mL/h, which is 24 L/h.
How do you convert L/100 km to km per litre?
Divide 100 by the fuel consumption. A car using 6.25 L/100 km travels 100 divided by 6.25, which is 16 km on each litre. To go back, divide 100 by the km per litre: 20 km/L is 100 divided by 20, which is 5 L/100 km.