Liters and milliliters
The amount of liquid a container can hold is its capacity. Larger amounts are measured in liters, written L, and small amounts in milliliters, written mL. Milli means a thousandth, so a milliliter is one thousandth of a liter: 1 L = 1000 mL.
This jug has a scale down each side. The left scale is in liters and the right scale is in milliliters. Filled to the top, the water reaches 1 on the left scale and 1000 on the right scale.
One level of water, read on two scales: 1 L on the left and 1000 mL on the right.
One level, two names
Pour some water out until the level is a quarter of the way up. The left scale now reads 0.25 L and the right scale reads 250 mL. The water was not changed into anything: it sits at one level, and the two scales give that amount two names.
A quarter of 1000 mL is 1000 ÷ 4 = 250 mL, so 0.25 L = 250 mL. In the same way, half a liter is 0.5 L = 500 mL, and three quarters of a liter is 0.75 L = 750 mL.
The level is a quarter of the way up: 0.25 L on the left and 250 mL on the right.
Three quarters of the way up: 0.75 L on the left and 750 mL on the right.
More than a liter
Every liter is another 1000 mL. 2 L is 2 × 1000 = 2000 mL, and 1 L 500 mL is 1000 + 500 = 1500 mL. To change liters to milliliters, multiply by 1000, just as for kilograms and grams.
The same works for a decimal of a liter: 0.85 L is 0.85 × 1000 = 850 mL. To change milliliters to liters, divide by 1000: 3600 mL is 3.6 L, or 3 L 600 mL.
A 2 L jug filled to 1.5 L holds 1500 mL, which is 1 L 500 mL.
A thousand, not a hundred
A liter is 1000 mL, not 100 mL. So half a liter is 500 mL, not 50 mL, and 0.85 L is 850 mL, not 85 mL.
Check the size of the answer. A milliliter is much smaller than a liter, so the number of milliliters must be much bigger than the number of liters: 2 L cannot be 200 mL, because 200 mL is only a fifth of one liter.
Worked example: A Drink Mixed in Liters and Poured into Glasses in Milliliters
Question Mrs Rahim mixes 3 liters 600 ml of water with 0.85 liters of syrup. She pours the drink into glasses that hold 300 ml each. (a) How many glasses can she fill completely? (b) How many milliliters of the drink are left over?
1.Write both amounts in milliliters: 3 liters 600 ml = 3600 ml and 0.85 liters = 850 ml.
In milliliters, the water is 3600 ml and the syrup is 0.85 × 1000 = 850 ml. 2.The total amount of drink is 3600 + 850 = 4450 ml.
The drink is 3600 + 850 = 4450 ml altogether. 3.Divide by the capacity of one glass. 300 × 14 = 4200 and 300 × 15 = 4500, which is more than 4450.
(a) 300 × 14 = 4200 fits in 4450 and 300 × 15 = 4500 does not: 14 glasses. 4.(a) She can fill 14 glasses completely.
5.(b) The amount left over is 4450 − 4200 = 250 ml.
(b) 4450 − 4200 = 250 ml is left over.
Answer: (a) 14 glasses; (b) 250 ml
Common mistakes
- Writing 0.85 liters as 85 ml. One liter is 1000 ml, so 0.85 liters is 0.85 × 1000 = 850 ml.
- Giving 15 glasses because 4450 ÷ 300 is nearly 15. The 15th glass would receive only 250 ml, so it is not filled completely.