#### Subtracting decimals

When subtracting decimal numbers, arrange the numbers so that the place value parts and the decimal points line up.

H | T | O | tenths | hundredths | thousandths | ||
---|---|---|---|---|---|---|---|

5 | 8 | 4 | . | 7 | 5 | 6 | |

− | 1 | 3 | 2 | . | 3 | 2 | 4 |

= | 4 | 5 | 2 | . | 4 | 3 | 2 |

Some subtractions require regrouping.

\(^4 5\hspace{-3mm}\color{red}/ \) | \(^1 4\) | 6 | . | \(^6 7\hspace{-3mm}\color{red}/ \) | \(^1 5\) | 9 | |

− | 2 | 8 | 0 | . | 2 | 8 | 7 |

= | 2 | 6 | 6 | . | 4 | 7 | 2 |

When there are different numbers of digits after the decimal point, such as in the example below, it is possible to become confused about what we should do with the space that is created by these 'ragged' decimals.

H | T | O | tenths | hundredths | ||
---|---|---|---|---|---|---|

3 | 7 | 8 | . | 5 | ||

− | 2 | 5 | 3 | . | 2 | 8 |

= |

Placing a zero to even up the lengths of the numbers doesn't alter the value of the number; it simply says that there are 'no hundredths'.

3 | 7 | 8 | . | \(^4 5\hspace{-3mm}\color{red}/ \) | \(^1 0\) | |

– | 2 | 5 | 3 | . | 2 | 8 |

= | 1 | 2 | 5 | . | 2 | 2 |