### Rounding Numbers + Scientific Notation (PPs)

*What is “Rounding” ?*

Rounding means reducing the digits in a number while trying to keep its value similar. *The result is less accurate, but easier to use. *

*Example:* 73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80.

**Common Method**

There are several different methods for rounding, but here we will only look at the **common method**, the one used by most people …

How to Round Numbers

- Decide which is the last digit to
**keep** - Leave it the same if the
**next digit**is less than 5 (this is called*rounding down*) - But increase it by 1 if the next digit is 5 or more (this is called
*rounding up*)

Example: Round 74 to the nearest 10

- We want to keep the “7” as it is in the 10s position
- The next digit is “4” which is less than 5, so no change is needed to “7”

**Answer: 70** ….. so (74 gets “rounded down”)

Example: Round 86 to the nearest 10

- We want to keep the “8”
- The next digit is “6” which is 5 or more, so increase the “8” by 1 to “9”

**Answer: 90** ….. (86 gets “rounded up”)

So: when the first digit **removed** is 5 or more, increase the last digit **remaining** by 1.

**Why does 5 go up ?**

5 is in the middle … so we **could** go up or down. But we need a method that everyone can agree to always use.

**Rounding Decimals**

First you need to know if you are rounding to tenths, or hundredths, etc. Or maybe to “so many decimal places”. That tells you how much of the number will be left when you finish.

Examples | Because … |
---|---|

3.1416 rounded to hundredths is 3.14 | … the next digit (1) is less than 5 |

1.2635 rounded to tenths is 1.3 | … the next digit (6) is 5 or more |

1.2635 rounded to 3 decimal places is 1.264 | … the next digit (5) is 5 or more |

**Rounding Whole Numbers**

You may want to round to tens, hundreds, etc, In this case you replace the removed digits with zero.

Examples | Because … |
---|---|

134.9 rounded to tens is 130 | … the next digit (4) is less than 5 |

12,690 rounded to thousands is 13,000 | … the next digit (6) is 5 or more |

1.239 rounded to units is 1 | … the next digit (2) is less than 5 |

**Rounding to Significant Digits**

To round “so many” significant digits, just **count digits from left to right**, and then round off from there.

Note: if there are leading zeros (such as 0.006), don’t count them because they are only there to show how small the number is.

Examples | Because … |
---|---|

1.239 rounded to 3 significant digits is 1.24 | … the next digit (9) is 5 or more |

134.9 rounded to 1 significant digit is 100 | … the next digit (3) is less than 5 |

0.0165 rounded to 2 significant digits is 0.017 | … the next digit (5) is 5 or more |

What follows is a PowerPoint presentation that will help you understand the content of the lesson in a better and easier way, (*pps*).