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Year 6 Maths Mass

Convert between metric units of mass - g & kg

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Theory

One kilogram is \(1000\) grams. To change kilograms to grams, multiply by 1000; to change grams to kilograms, divide by 1000. This Year 6 maths page shows how to convert whole and decimal masses, such as \(3.6\) kg \(= 3600\) g, and how to compare, order and add masses written in different units.

Mass is how heavy something is. A gram (g) is about the mass of a paper clip; a kilogram (kg) is about the mass of a 1 litre bottle of water.

Kilo means one thousand, so \(1\) kg \(= 1000\) g.

kg to g: multiply by \(1000\); the digits move \(3\) places left. \(3.6\) kg \(= 3600\) g, \(0.08\) kg \(= 80\) g.

g to kg: divide by \(1000\); the digits move \(3\) places right. \(4500\) g \(= 4.5\) kg, \(45\) g \(= 0.045\) kg.

A mass such as \(2\) kg \(300\) g means \(2000 + 300 = 2300\) g, which is \(2.3\) kg.

Kilograms to grams machine A machine: kilograms times 1000 gives grams. A red arrow back underneath divides by 1000 to go from grams to kilograms. kg g × 1000 ÷ 1000
kg \(\to\) g: \(\times 1000\). g \(\to\) kg: \(\div 1000\).
Kitchen scale reading 1700 grams A dial scale from 0 to 2000 grams, numbered every 500 with small marks every 100 grams. The red pointer is two small marks past 1500, at 1700 grams. 0500100015002000 grams
The pointer shows \(1700\) g, which is \(1.7\) kg.
Matching kilograms and grams Two parallel number lines from 0 to 1 kilogram. The ticks line up: 0, 0.25, 0.5, 0.75 and 1 kilogram match 0, 250, 500, 750 and 1000 grams. kg 0 0.25 0.5 0.75 1 g 0 250 500 750 1000
Half a kilogram is \(500\) g; a quarter of a kilogram is \(250\) g.

Grams and kilograms:

\[ 1\text{ kg} = 1000\text{ g} \]
1 kg =1000 g
\[ \text{kg} \times 1000 = \text{g} \qquad \text{g} \div 1000 = \text{kg} \]
kg ×1000= g , g ÷1000= kg
KilogramsGrams
\(0.1\) kg\(100\) g
\(0.25\) kg\(250\) g
\(0.5\) kg\(500\) g
\(1.5\) kg\(1500\) g
\(3.04\) kg\(3040\) g
Three places. Multiplying or dividing by \(1000\) moves the digits three places. Fill empty places with zeros: \(0.08\) kg \(= 80\) g.
Same unit first. To compare, order or add masses, write them all in grams (or all in kilograms) first.

How to convert a mass

  1. Decide: is the new unit smaller (kg to g, multiply) or larger (g to kg, divide)?
  2. Multiply or divide by \(1000\).
  3. Check: grams should be the bigger number.

How to compare or add masses

  1. Change every mass to grams.
  2. Compare, order or add the numbers of grams.
  3. Change back to kilograms if the question asks.
Example 1 — kg to g
How many grams are in \(6\) kg?
Solution
\(6 \times 1000\)\(=\)\(6000\)
6×1000=6000

\(6000\) g.

Example 2 — g to kg
Write in kilograms.
(i) \(7000\) g
(ii) \(4500\) g
Solution
\(7000 \div 1000\)\(=\)\(7\)
\(4500 \div 1000\)\(=\)\(4.5\)
7 kg ,4.5 kg

(i) \(7\) kg
(ii) \(4.5\) kg

Example 3 — Decimal kilograms
Write in grams.
(i) \(3.6\) kg
(ii) \(0.35\) kg
(iii) \(0.08\) kg
Solution
\(3.6 \times 1000\)\(=\)\(3600\)
\(0.35 \times 1000\)\(=\)\(350\)
\(0.08 \times 1000\)\(=\)\(80\)
3600 g ,350 g ,80 g

(i) \(3600\) g
(ii) \(350\) g
(iii) \(80\) g

Example 4 — Grams to decimal kilograms
Write in kilograms.
(i) \(2750\) g
(ii) \(600\) g
(iii) \(45\) g
Solution
\(2750 \div 1000\)\(=\)\(2.75\)
\(600 \div 1000\)\(=\)\(0.6\)
\(45 \div 1000\)\(=\)\(0.045\)
2.75 kg ,0.6 kg ,0.045 kg

(i) \(2.75\) kg
(ii) \(0.6\) kg
(iii) \(0.045\) kg

Example 5 — Kilograms and grams
Write \(4\) kg \(65\) g in grams and in kilograms.
Solution
\(4 \times 1000 + 65\)\(=\)\(4065\)
4×1000+65=4065

\(4065\) g, which is \(4.065\) kg.

Example 6 — Which is heavier?
Bag A holds \(1.6\) kg of rice and bag B holds \(1580\) g.
(i) Which bag is heavier?
(ii) By how many grams?
Solution
\(1.6 \times 1000\)\(=\)\(1600\)
\(1600 - 1580\)\(=\)\(20\)
1600−1580=20

(i) Bag A
(ii) \(20\) g

Example 7 — Order
Order from lightest to heaviest: \(2.3\) kg, \(2080\) g, \(2.25\) kg, \(2400\) g.
Solution

In grams: \(2300\), \(2080\), \(2250\), \(2400\).

\(2080\) g, \(2.25\) kg, \(2.3\) kg, \(2400\) g.

Example 8 — Add masses
A damper recipe uses \(1.75\) kg of flour, \(350\) g of milk powder and \(0.2\) kg of butter. What is the total mass in grams and in kilograms?
Solution
\(1750 + 350 + 200\)\(=\)\(2300\)
1750+350+200=2300

\(2300\) g, which is \(2.3\) kg.

Example 9 — Find the mistake
Leo changed \(4200\) g to kilograms by dividing by \(100\) and wrote \(42\) kg. What is right?
Solution
\(4200 \div 1000\)\(=\)\(4.2\)
4200÷1000=4.2

A kilogram is \(1000\) g, so divide by \(1000\): \(4.2\) kg.

Common pitfalls

Dividing by 10 or 100. There are \(1000\) g in a kilogram, so \(4200\) g is \(4.2\) kg, not \(42\) kg or \(420\) kg.
Multiplying the wrong way. Grams to kilograms makes the number smaller, so divide.
Missing zeros. \(65\) g is \(0.065\) kg; \(0.08\) kg is \(80\) g.
Comparing different units. \(1580\) g is less than \(1.6\) kg, even though \(1580\) looks bigger.

Frequently asked questions

How many grams are in a kilogram?

\(1000\).

How do I change kilograms to grams?

Multiply by \(1000\): \(3.6\) kg \(= 3600\) g.

How do I change grams to kilograms?

Divide by \(1000\): \(4500\) g \(= 4.5\) kg.

What is half a kilogram in grams?

\(500\) g.

How do I add 1.75 kg and 350 g?

Change to grams first: \(1750 + 350 = 2100\) g, which is \(2.1\) kg.

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