Unit Conversions

Worked example

1. 1

   $4.7\text{ m}\to \text{cm}$ — The question. A centimetre is smaller than a metre, so you need more of them: multiply.

2. 2

   $4.7\times 100=470\text{ cm}$ — There are 100 cm in each metre, so multiply by 100. Move each digit two places left.

3. 3

   $3800\text{ g}\to \text{kg}$ — A new question. A kilogram is bigger than a gram, so you need fewer of them: divide.

4. 4

   $3800÷1000=3.8\text{ kg}$ — There are 1000 g in each kilogram, so divide by 1000. Move each digit three places right.

Worked example

1. 1

   $0.052\times 1000=52\text{ m}$ — Pick metres as the one unit. A metre is smaller than a kilometre, so multiply by 1000.

2. 2

   $512÷100=5.12\text{ m}$ — A metre is bigger than a centimetre, so divide by 100.

3. 3

   $5150÷1000=5.15\text{ m}$ — There are 1000 mm in a metre, so divide by 1000.

4. 4

   $5\frac{1}{4}\text{ m}=5.25\text{ m}$ — Write the fraction as a decimal: a quarter is 0.25. Now all four are in metres.

5. 5

   $5.12<5.15<5.25<52$ — Compare the numbers. 52 m is by far the biggest, even though 0.052 looked tiny.

6. 6

   $512\text{ cm},5150\text{ mm},5\frac{1}{4}\text{ m},0.052\text{ km}$ — Write the answer with the original values, in that order. That is what the question asked for.

Worked example

1. 1

   $0.7\times 1000=700\text{ g}$ — Change the kilograms into grams, so both sides have the same unit.

2. 2

   $700\text{ g}>70\text{ g}$ — 700 is bigger than 70, so 0.7 kg > 70 g.

Worked example

1. 1

   $2\text{ litres}=2000\text{ ml}$ — The cup is in millilitres, so change the juice to the same unit. 1 litre = 1000 ml, so multiply by 1000.

2. 2

   $2000÷450=4.44\dots$ — Divide the total by the size of one cup. This says how many cups the juice could fill.

3. 3

   $4\text{ full cups}$ — Keep only the whole number. The 0.44 is part of a cup, not a full one, so round down.

4. 4

   $4\times 450=1800\text{ ml}$ — Multiply the full cups by the size of one cup. This is the juice used.

5. 5

   $2000-1800=200\text{ ml}$ — Take the juice used away from the total. What remains is the answer.

Worked example

1. 1

   $72\text{ km/h}$ — The question. It means the car goes 72 km in one hour.

2. 2

   $72\times 1000=72000\text{ m}$ — Change the distance first. There are 1000 m in a km, so 72 km = 72 000 m.

3. 3

   $1\text{ hour}=3600\text{ s}$ — Now the time. One hour is 60 minutes and each minute is 60 seconds, so 60 × 60 = 3600.

4. 4

   $72000÷3600=20\text{ m/s}$ — Share the metres over the seconds. This gives the metres in one second.

Worked example

1. 1

   $15\text{ m/s}$ — The question. It means 15 m in every second.

2. 2

   $15\times 3600=54000\text{ m}$ — An hour has 3600 seconds, so in one hour it goes 3600 times as far.

3. 3

   $54000÷1000=54\text{ km/h}$ — Change metres into kilometres. A km is bigger, so divide by 1000.

Worked example

1. 1

   $C=120$ — The question gives Celsius, so put it into the formula to find Fahrenheit.

2. 2

   $F=1.8\times 120+32$ — Swap C for 120. Nothing else in the formula changes.

3. 3

   $F=216+32$ — Multiply first: 1.8 × 120 = 216. Order of operations puts × before +.

4. 4

   $F=248$ — Then add the 32.

Worked example

1. 1

   $356=1.8C+32$ — Now Fahrenheit is given, so put 356 in place of F and solve for C.

2. 2

   $324=1.8C$ — Take away 32 from both sides: 356 − 32 = 324. The +32 was done last, so undo it first.

3. 3

   $C=324÷1.8=180$ — Then divide both sides by 1.8 to leave C on its own.

4. 4

   $1.8\times 180+32=356$ — Check by putting 180 back in. It gives 356, so the answer is right.

Worked example

1. 1

   $4\times 1.609344=6.437376\text{ km}$ — Each mile is 1.609344 km, so 4 miles is 4 times as much. Keep every digit for now.

2. 2

   $6.437376\times 1000=6437.376\text{ m}$ — The question wants metres. A metre is smaller, so multiply by 1000.

3. 3

   $6437.376\approx 6437\text{ m}$ — Round only at the end. The next digit is 3, so round down to the nearest metre.

Worked example

1. 1

   $250\text{ m/min}$ — The question. It means 250 m in every minute.

2. 2

   $250\times 60=15000\text{ m}$ — There are 60 minutes in an hour, so in one hour it goes 60 times as far.

3. 3

   $15000÷1000=15\text{ km/h}$ — Change metres into kilometres: divide by 1000.