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`
