Multiplying by 10, 100, 1000, moves the digits in each column (units, 10s, 100s, etc) to the left:

• multiplying by 10 moves all the digits 1 column to the left;

• multiplying by 100 moves the digits 2 columns to the left;

• multiplying by 1000 moves the digits 3 columns to the left.

10 000 | 1 000 | 100 | 10 | 1 | |
---|---|---|---|---|---|

2 | 6 | ||||

2 | 6 | 0 | x10 | ||

2 | 6 | 0 | 0 | x100 | |

2 | 6 | 0 | 0 | 0 | x1000 |

Dividing by 10, 100, 1000 moves the digits in each column to the right:

• dividing by 10 moves them 1 digit to the right;

• dividing by 100 is 2 digits right;

• dividing by 1000 is 3 digits right.

10 000 | 1 000 | 100 | 10 | 1 | |
---|---|---|---|---|---|

4 | 9 | 0 | 0 | 0 | |

4 | 9 | 0 | 0 | ÷10 | |

4 | 9 | 0 | ÷100 | ||

4 | 9 | ÷1000 |

The same is true for decimal numbers. The digits move and the decimal point stays in the same place.

1000 | 100 | 10 | 1 | `frac(1)(10)` | `frac(1)(100)` | `frac(1)(1000)` | ||
---|---|---|---|---|---|---|---|---|

3 | . | 0 | 1 | 2 | ||||

3 | 0 | . | 1 | 2 | 0 | x10 | ||

3 | 0 | 1 | . | 2 | x100 | |||

3 | 0 | 1 | 2 | . | 0 | x1000 |

100 | 10 | 1 | `frac(1)(10)` | `frac(1)(100)` | ||
---|---|---|---|---|---|---|

4 | 9 | 0 | . | 0 | ||

4 | 9 | . | 0 | ÷10 | ||

4 | . | 9 | ÷100 | |||

0 | . | 4 | 9 | ÷1000 |

What is 34 x 100?

Move the 34 two digits to the left, filling the empty spaces with zeroes.

Answer: 3400

Given 34 x 23 = 782, what is 34 x 230?

230 = 23 x 10, re-write the question as 34 x 23 x 10.

That makes the answer 10 times larger than the original question.

Answer: 7820

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