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How to multiply or divide by 10, 100, or 1000 using place value

Part of MathsPlace value

Key points

  • can be used to multiply or divide whole numbers by 10, 100 or 1,000
  • When multiplying, each digit moves to the left.
  • When dividing, each digit moves to the right.
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Multiplying by 10, 100 and 1,000

can be helpful when multiplying by 10, 100 and 1,000. When multiplying by a power of 10 (eg 10, 100, 1,000) are needed to make sure that the number is written correctly.

Multiplying by 10

  • To multiply by 10, each digit moves one place to the left. Eg, units become tens.

Multiplying by 100

  • To multiply by 100, each digit moves two places to the left. Eg, units become hundreds.

Multiplying by 1,000

  • To multiply by 1,000, each digit moves three places to the left. Eg, units become thousands.

Note: units are often referred to as ones. For example, 34 has 3 tens and 4 units, or we could say 34 has 3 tens and 4 ones.

Example: multiplying by 10, 100 and 1,000

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  1. Example 1: Multiplying by 10. Place value showing 26 with units, tens and a blank hundreds label. Below: 26 multiplied by 10.

    Write 26 out with place value labels. To multiply 26 by 10, move each digit one place to the left.

Question

What is 14 x 1,000?

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Dividing by 10, 100 and 1,000

Place value can be helpful when dividing by 10, 100 and 1,000. Dividing by a power of 10 (eg 10, 100, 1,000) can lead to a series of zeros after the decimal point which don’t need to be recorded.

Dividing by 10

  • When dividing by 10, each digit moves one place to the right. Eg, Thousands become hundreds, hundreds become tens and tens become units.

Dividing by 100

  • When dividing by 100, each digit moves two places to the right. Thousands become tens, hundreds become units, and tens and units become fractions of a unit.

Dividing by 1,000

  • When dividing by 1,000, each digit moves three places to the right. Thousands become units. Hundreds, tens, and units become fractions of a unit.

Example: dividing by 10, 100 and 1,000

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  1. Example 1: Dividing by 10. Four hundred and sixty written with place value labels hundreds, tens, and units. Below: four hundred and sixty divided by 10.

    Write 460 out with place value labels. To divide 460 by 10, move each digit one place to the right.

Question

What is 47,000 ÷ 100?

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Practise multiplying and dividing by 10, 100 and 1,000

Quiz

Practise what you've learned about multiplying and dividing by 10, 100 and 1,000 with this quiz.

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Real-world maths

People may use multiplying or dividing by 10, 100 or 1,000 to work out the cost of different items.

Person playing with a games controller
Expensive items like games consoles can be paid for in a number of instalments.

Expensive items are not always paid for in full. Sometimes they are paid for in a number of instalments. For example, a games console costs £450.

A person may want to split their payment over 10 months to make it more affordable. They would need to be able to divide £450 by 10 to calculate the monthly payments.

A shop owner may use this method to calculate profits. For example, they know that they make £2 profit for each box of chocolates they sell. If they sell 100 boxes in a month, they need to multiply by 100. 100 x £2 = £200 profit.

Person playing with a games controller
Expensive items like games consoles can be paid for in a number of instalments.
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Using your maths skills, help to build bridges and bring light back to the islands in this free game from ý Bitesize.

Play the Divided Islands game!
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