Multiply & divide decimals by 10, 100, 1000 - Divide by 10,100,1000
Theory
Dividing by \(10\), \(100\) or \(1000\) makes a number smaller. Every digit moves one, two or three places to the right; the decimal point stays still. This Year 6 maths page shows how to place zeros after the point and use division to convert units.
\(\div 10\): each digit moves one place right. \(\div 100\): two places. \(\div 1000\): three places.
If digits move past the point, write a \(0\) in the ones place and fill any gaps after the point with zeros: \(4 \div 1000 = 0.004\).
Dividing by \(10\) finds one tenth; dividing by \(100\) finds one hundredth.
Unit conversions: \(\text{cm} \to \text{m}\) is \(\div 100\); \(\text{g} \to \text{kg}\), \(\text{mL} \to \text{L}\) and \(\text{m} \to \text{km}\) are \(\div 1000\).
How far the digits move:
Dividing by 10, 100 or 1000
- Count the zeros in the divisor.
- Move every digit that many places to the right.
- Write a \(0\) in the ones place if needed and fill gaps with zeros.
| \(47 \div 10\) | \(=\) | \(4.7\) |
\(4.7\).
| \(3.6 \div 100\) | \(=\) | \(0.036\) |
\(0.036\).
| \(520 \div 1000\) | \(=\) | \(0.52\) |
\(0.52\).
(i) \(0.8 \div 10\)
(ii) \(4 \div 1000\)
(iii) \(650 \div 100\)
(i) \(0.08\)
(ii) \(0.004\)
(iii) \(6.5\)
| \(75 \div 100\) | \(=\) | \(0.75\) |
\(0.75\) m.
| \(2400 \div 1000\) | \(=\) | \(2.4\) |
\(2.4\) L.
(i) What is one tenth of it?
(ii) What is one hundredth of it?
| \(650 \div 10\) | \(=\) | \(65\) |
| \(650 \div 100\) | \(=\) | \(6.5\) |
(i) \(65\) L
(ii) \(6.5\) L
| \(0.37 \times 100\) | \(=\) | \(37\) |
\(37\).
Common pitfalls
Frequently asked questions
What happens when you divide by 100?
Every digit moves two places to the right.
What is 4 ÷ 1000?
\(0.004\).
How do I change centimetres to metres?
Divide by \(100\): \(75\) cm \(= 0.75\) m.
How do I find one tenth of an amount?
Divide by \(10\): one tenth of \(650\) is \(65\).
Why are zeros needed after the point?
They hold the empty places so each digit keeps its value.