# Rounding and difficult nines

When rounding up 9's you have to be careful.

If you round a `9` to `10` think of it as adding `9+1`

`9` |

`+1` |

`10` |

You put a zero in the first column and add `1` to the next.

**Example 1**

Round `43.299` to two decimal places.

You would answer this as follows:

`43.299` round to two decimal places

`43.2ul9\9` underline the digit (of `2^(nd)` decimal place)

`43.2ul9\9` look next door

`9` It's five or more so you raise the score (round up)

`43.2cancel9` `9` becomes `10`

`43.30` add `1` to the next column and put a zero in the last column.

Answer:

`43.299` rounded to 2 D.P. `=43.30`

**Example 2**

Round `34.997` to two decimal places.

You would answer this as follows:

`34.997` round to two decimal places

`34.9ul9\7` underline the digit (of `2^(nd)` decimal place)

`34.9ul9\7` look next door

`7` It's five or more so you raise the score (round up)

`34.9cancel9` `9` becomes `10`

`34.cancel9cancel9` But if you add `1` to the next column that becomes `10`.

`35.00` Add one to the next column.

Answer:

`34.997` rounded to 2 D.P. `=35.00`

**Example 3**

Round `£19.90` to the nearest `£1.00`

Answer as follows:

`£19.90` rounded to the nearest unit of `1`

`1ul9\.90` underline the digit (units `1`)

`1ul9\.90` look next door

`9` It's five or more so you raise the score (round up)

`1cancel9` `9` becomes `10`

`20` Add `1` to the next column and put a zero in the last column.

Answer:

`£19.90` rounded to the nearest `£1.00` is `£20`

**Example 4**

Round `£99.98` to the nearest `£1.00`

`£99.98` round to the nearest unit of `1`

`9ul9\.98` underline the digit (units `1`)

`9ul9\.98` look next door

`9` It's five or more so raise the score (round up)

`9cancel9` `9` becomes `10`

`cancel9cancel9` But if we add one to the next column that becomes `10`

`100` Add one to the next column.

Answer:

`£99.98` to the nearest `£1.00` is `£100`

**Example 5**

Round `5.9999` to `3` decimal places

Answer as follows:

Round `5.9999` to 3 D.P.

`5.99ul9\9` underline the digit (3 D.P.)

`599ul9\9` look next door

`9` It's five or more so you raise the score (round up)

`5.99cancel9` `9` becomes `10`

`5.cancel9cancel9cancel9` but if you add one to the next column that becomes `10`

`6.000` now add one to the next column.

Answer:

`5.9999` to `3` decimal places is `6.000`

# Rounding and difficult nines

When rounding up 9's you have to be careful.

If you round a `9` to `10` think of it as adding `9+1`

`9` |

`+1` |

`10` |

You put a zero in the first column and add `1` to the next.

**Example 1**

Round `43.299` to two decimal places.

You would answer this as follows:

`43.299` round to two decimal places

`43.2ul9\9` underline the digit (of `2^(nd)` decimal place)

`43.2ul9\9` look next door

`9` It's five or more so you raise the score (round up)

`43.2cancel9` `9` becomes `10`

`43.30` add `1` to the next column and put a zero in the last column.

Answer:

`43.299` rounded to 2 D.P. `=43.30`

**Example 2**

Round `34.997` to two decimal places.

You would answer this as follows:

`34.997` round to two decimal places

`34.9ul9\7` underline the digit (of `2^(nd)` decimal place)

`34.9ul9\7` look next door

`7` It's five or more so you raise the score (round up)

`34.9cancel9` `9` becomes `10`

`34.cancel9cancel9` But if you add `1` to the next column that becomes `10`.

`35.00` Add one to the next column.

Answer:

`34.997` rounded to 2 D.P. `=35.00`

**Example 3**

Round `£19.90` to the nearest `£1.00`

Answer as follows:

`£19.90` rounded to the nearest unit of `1`

`1ul9\.90` underline the digit (units `1`)

`1ul9\.90` look next door

`9` It's five or more so you raise the score (round up)

`1cancel9` `9` becomes `10`

`20` Add `1` to the next column and put a zero in the last column.

Answer:

`£19.90` rounded to the nearest `£1.00` is `£20`

**Example 4**

Round `£99.98` to the nearest `£1.00`

`£99.98` round to the nearest unit of `1`

`9ul9\.98` underline the digit (units `1`)

`9ul9\.98` look next door

`9` It's five or more so raise the score (round up)

`9cancel9` `9` becomes `10`

`cancel9cancel9` But if we add one to the next column that becomes `10`

`100` Add one to the next column.

Answer:

`£99.98` to the nearest `£1.00` is `£100`

**Example 5**

Round `5.9999` to `3` decimal places

Answer as follows:

Round `5.9999` to 3 D.P.

`5.99ul9\9` underline the digit (3 D.P.)

`599ul9\9` look next door

`9` It's five or more so you raise the score (round up)

`5.99cancel9` `9` becomes `10`

`5.cancel9cancel9cancel9` but if you add one to the next column that becomes `10`

`6.000` now add one to the next column.

Answer:

`5.9999` to `3` decimal places is `6.000`