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Year 6 Maths Decimals

Multiply & divide decimals by 10, 100, 1000 - Multiply by 10,100,1000

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Theory

Multiplying by \(10\), \(100\) or \(1000\) makes a number \(10\), \(100\) or \(1000\) times bigger. Every digit moves one, two or three places to the left; the decimal point stays still. This Year 6 maths page shows the place value chart, placeholder zeros and conversions.

\(\times 10\): each digit moves one place left. \(\times 100\): two places. \(\times 1000\): three places.

The number of places moved equals the number of zeros in \(10\), \(100\) or \(1000\).

If digits move past the end, fill the empty places with zeros: \(4.7 \times 100 = 470\).

Unit conversions use this: \(\text{m} \to \text{cm}\) is \(\times 100\); \(\text{kg} \to \text{g}\), \(\text{L} \to \text{mL}\) and \(\text{km} \to \text{m}\) are \(\times 1000\).

Multiplying 0.36 by 10 A place value chart. The top row shows 0.36; the bottom row shows 3.6. Each digit has moved one place to the left while the decimal point stays still. ThHTOthth 036 36 start× 10 The decimal point stays still; the digits move.
\(0.36 \times 10 = 3.6\): every digit moves one place left.
Multiplying 0.052 by 1000 A place value chart. The top row shows 0.052; the bottom row shows 52. Each digit has moved three places to the left. ThHTOthth 0052 25 start× 1000 The decimal point stays still; the digits move.
\(0.052 \times 1000 = 52\): three places left.

How far the digits move:

\[ \times 10 \Rightarrow 1 \text{ place left} \]
×101 place left
\[ \times 100 \Rightarrow 2 \text{ places left} \]
×1002 places left
\[ \times 1000 \Rightarrow 3 \text{ places left} \]
×10003 places left
The point stays still. It is the digits that move.
Not "add a zero". \(0.6 \times 100\) is \(60\), not \(0.600\).

Multiplying by 10, 100 or 1000

  1. Count the zeros: that is how many places to move.
  2. Move every digit that many places to the left.
  3. Fill empty places before the point with zeros; drop leading zeros.
Example 1 — Times 10
Calculate \(0.36 \times 10\).
Solution
\(0.36 \times 10\)\(=\)\(3.6\)
0.36×10=3.6

\(3.6\).

Example 2 — Times 100
Calculate \(4.7 \times 100\).
Solution
\(4.7 \times 100\)\(=\)\(470\)
4.7×100=470

Two places left, with a zero in the ones place: \(470\).

Example 3 — Times 1000
Calculate \(0.052 \times 1000\).
Solution
\(0.052 \times 1000\)\(=\)\(52\)
0.052×1000=52

\(52\).

Example 4 — Several
Calculate.
(i) \(0.09 \times 100\)
(ii) \(3.08 \times 10\)
(iii) \(0.6 \times 100\)
Solution

(i) \(9\)
(ii) \(30.8\)
(iii) \(60\)

Example 5 — Metres to centimetres
A shelf is \(2.75\) m long. How long is it in centimetres?
Solution
\(2.75 \times 100\)\(=\)\(275\)
2.75×100=275 cm

\(275\) cm.

Example 6 — Kilograms to grams
Convert \(1.8\) kg to grams.
Solution
\(1.8 \times 1000\)\(=\)\(1800\)
1.8×1000=1800 g

\(1800\) g.

Example 7 — Missing number
A number times \(1000\) is \(730\). What was the number?
Solution
\(730 \div 1000\)\(=\)\(0.73\)
730÷1000=0.73

\(0.73\). Check: \(0.73 \times 1000 = 730\).

Example 8 — Find the mistake
Eli wrote \(0.6 \times 100 = 0.600\). What went wrong?
Solution

Adding zeros after the decimal part does not change the value. The digits move two places left: \(60\).

Common pitfalls

Adding zeros to the end of a decimal. \(0.6\) and \(0.600\) are equal; that is not multiplying.
Moving the wrong number of places. Count the zeros in the multiplier.
Moving right instead of left. Multiplying by 10, 100 or 1000 makes the number bigger.
Wrong conversion factor. m to cm is \(\times 100\); kg to g is \(\times 1000\).

Frequently asked questions

What happens to the digits when you multiply by 10?

Each digit moves one place to the left.

Does the decimal point move?

Think of the point as fixed; the digits move.

What is 4.7 × 100?

\(470\).

How do I change metres to centimetres?

Multiply by \(100\): \(2.75\) m \(= 275\) cm.

Why not just add zeros?

Zeros after the decimal part do not change a decimal: \(0.6 = 0.60\).

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