Multiplying and dividing a number by 10, 100 and 1,000 | Maths

Starter quiz

Match the factors to their product.

5 × 10 =

⇔

50 ✓

60 × 10 =

⇔

600 ✓

800 ÷ 10 =

⇔

80 ✓

8,000 ÷ 10 =

⇔

800 ✓

400 ÷ 10 =

⇔

40 ✓
Match the equation to the correct product or quotient.

5 × 100 =

⇔

500 ✓

60 × 100 =

⇔

6,000 ✓

800 ÷ 100 =

⇔

8 ✓

8,000 ÷ 100 =

⇔

80 ✓

500 ÷ 100 =

⇔

5 ✓
Look at the images of base 10 blocks and complete the sentence. There are ______ tenths in one whole.

'ten' ✓
Look at the images of base 10 blocks and complete the sentence. There are ______ hundredths in one whole.

'100' ✓
Look at the images of base 10 blocks and complete the sentence. There are ______ hundredths in one tenth.

'ten' ✓
Dividing by 10 is the same as multiplying by ______

'0.1' ✓

Exit quiz

One-thousandth is composed of ______ parts of one-hundredth.

'10' ✓
Which equations can be formed from this statement? One tenth has been divided into 100 equal parts. Each part is one thousandth of the whole.

0.1 ÷ 10 = 0.01

1 × 0.001 = 0.001

0.1 ÷ 100 = 0.01

0.1 ÷ 100 = 0.001 ✓

0.1 × 0.01 = 0.001 ✓
When a number is multiplied by 1,000, the digits move ______ places to the left.

'3' ✓
Use the Gattegno chart to complete the sentence. 0.001 is ______ times smaller than 0.1

1

10

100 ✓

1,000
Match the division expression to its equivalent multiplication expression.

1 ÷ 10

⇔

1 × 0.1 ✓

0.1 ÷ 10

⇔

0.1 × 0.1 ✓

1 ÷ 1,000

⇔

1 × 0.001 ✓

0.01 ÷ 100

⇔

0.01 × 0.01 ✓

0.1 ÷ 1

⇔

0.1 × 1 ✓
Match the equations to their product.

5 × 1,000 =

⇔

5,000 ✓

5000 ÷ 1,000 =

⇔

5 ✓

6,000 × 0.001 =

⇔

6 ✓

5,000 × 0.1 =

⇔

500 ✓

6,000 ÷ 100 =

⇔

60 ✓

5,000 × 0.01 =

⇔

50 ✓

Worksheet

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Lesson Details

Key learning points

To multiply a number by 1,000 move the digits three places to the left - this makes the number 1,000 times the size.
To divide a number by 1,000 move the digits three places to the right - this makes the numbers 1,000th times the size.
A place value chart can be used to explain how the digits move when you multiply or divide by 10, 100 and 1,000.
Use a Gattengo chart can be used to explain how the digits move when you multiply divide by 10, 100 and 1,000.
Dividing by 10, 100 or 1,000 is equivalent to multiplying by 0.1, 0.01 or 0.001 respectively.

Common misconception

Children may confuse use of the Base 10 equipment. They may also confuse the equivalence between dividing by 10/100/1,000 and multiplying by 0.1/0.01/0.001.

The large cube now represents one whole. The smaller blocks represent decimal fraction numbers. Use stem sentences to support common mistakes: when a number is divided by ___, it is the same as multiplying by ___

Keywords

Thousandth - One-thousandth is one part in one thousand equal parts.
Equivalent - If something is equivalent, it has the same value. For example, £1 is equivalent to 100 p - they have the same value.