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Primary - Stage 3 (Year 5 & 6) Stage 3 (Year 5 & 6) 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 \(1000\).

A gram (g) and a kilogram (kg) are metric units of mass. The prefix kilo means a thousand, so \(1\text{ kg} = 1000\text{ g}\).

To change kilograms to grams, multiply by \(1000\). A gram is smaller, so it takes more of them and the number gets bigger.

To change grams to kilograms, divide by \(1000\). A kilogram is larger, so fewer are needed and the number gets smaller.

\(1\text{ kg} = 1000\text{ g}\). This one fact drives every conversion between grams and kilograms.
Converting between grams and kilograms Grams to kilograms divides by 1000; kilograms to grams multiplies by 1000. gkg ÷1000 ×1000
To a smaller unit (kg \(\rightarrow\) g), \(\times 1000\); to a larger unit (g \(\rightarrow\) kg), \(\div 1000\). For example \(3\text{ kg} = 3000\text{ g}\).

Every step multiplies or divides by \(1000\).

KilogramsGrams
\(1\) kg\(1000\) g
\(2\) kg\(2000\) g
\(2.5\) kg\(2500\) g
\(0.5\) kg\(500\) g
\(9\) kg\(9000\) g

Converting grams and kilograms

  1. Decide the direction: which unit are you changing to?
  2. To grams (the smaller unit), multiply by \(1000\).
  3. To kilograms (the larger unit), divide by \(1000\).
  4. Check: to a smaller unit the number grows; to a larger unit it shrinks.
Example 1 — Kilograms to grams
Change \(3\) kg to grams.
Solution

A gram is smaller, so multiply.

\(3 \times 1000\)\(=\)\(3000\)

So \(3\text{ kg} = 3000\) g.

Example 2 — Grams to kilograms
Write \(5000\) g in kilograms.
Solution

A kilogram is larger, so divide.

\(5000 \div 1000\)\(=\)\(5\)

So \(5000\text{ g} = 5\) kg.

Example 3 — A decimal mass
What is \(2.5\) kg in grams?
Solution

Multiply by \(1000\).

\(2.5 \times 1000\)\(=\)\(2500\)

So \(2.5\text{ kg} = 2500\) g.

Example 4 — Which calculation
Which calculation changes grams into kilograms?
Solution

A kilogram is the larger unit.

grams \(\div 1000\)\(=\)kilograms

Divide by \(1000\).

Common pitfalls

Multiplying when you should divide. To a smaller unit the number grows, so multiply; to a larger unit it shrinks, so divide.
Using \(100\) instead of \(1000\). A kilogram is a thousand grams, so the factor is always \(1000\).
Slipping on decimals. \(2.5\) kg is \(2.5 \times 1000 = 2500\) g, not \(250\) g.

Frequently asked questions

How many grams are in a kilogram?

\(1000\). The prefix kilo means a thousand, so \(1\text{ kg} = 1000\text{ g}\).

How do I change kilograms to grams?

Multiply by \(1000\), because a gram is smaller. For example \(3\text{ kg} = 3 \times 1000 = 3000\) g.

How do I change grams to kilograms?

Divide by \(1000\), because a kilogram is larger. For example \(5000\text{ g} = 5000 \div 1000 = 5\) kg.

What is \(2.5\) kg in grams?

\(2500\) g. Multiply by \(1000\): \(2.5 \times 1000 = 2500\).

Why does the number get bigger when I change to grams?

A gram is smaller than a kilogram, so it takes many more of them to make the same mass. That is why the number grows.

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