What is 45.546 to 3 decimal places?
Explanation
When we express a number to a specific number of decimal places, we're showing the number with exactly that many digits after the decimal point. This is different from rounding.
In this case, we're expressing 45.546 to 3 decimal places.
The process involves:
- Keeping all digits up to the specified decimal place
- Dropping any digits beyond that point
- Not rounding based on the dropped digits
In this case:
- The original number is 45.546
- We're rounding to 3 decimal places
- The 3rd digit after the decimal point is 6
- The next digit is 0
- Since the next digit (0) is less than 5, we round down.
Expressing 45.546 to Various Decimal Places
Since the input number has more than two decimal places, here's how it looks when expressed to different decimal places:
| Decimal Places | Expressed Value | Explanation |
|---|---|---|
| 2 | 45.55 | Truncated at the 2nd decimal place. |
| 3 | 45.546 | Shown in full, with additional zeros if necessary. |
| 4 | 45.5460 | Shown in full, with additional zeros if necessary. |
| 5 | 45.54600 | Shown in full, with additional zeros if necessary. |
| 6 | 45.546000 | Shown in full, with additional zeros if necessary. |
| 7 | 45.5460000 | Shown in full, with additional zeros if necessary. |
Notice how the number changes as we increase the number of decimal places. This demonstrates the concept of precision in decimal representations.
Examples of Expressing Numbers to Different Decimal Places
| Original Number | Decimal Places | Expressed Result | Note |
|---|---|---|---|
| 45.546 | 3 | 45.546 | Original input |
| 45.546 | 4 | 45.5460 | One more decimal place |
| 45.54921 | 3 | 45.549 | Slightly modified number |
| 45.546 | 2 | 45.55 | One less decimal place |
If We Round 7.24 rounded to 1 decimal place :
45.546 rounded to 3 decimal places is: 45.546Explanation
When we round a number to a specific decimal place, we're adjusting it to the nearest value with the desired precision. In this case, we're rounding 45.546 to 3 decimal places.
The process involves looking at the digit immediately to the right of the desired decimal place. If this digit is 5 or greater, we round up. Otherwise, we round down.
Expressing to Decimal Places vs. Rounding
It's important to understand the difference between expressing a number to a certain number of decimal places and rounding to that number of decimal places:
- Expressing to decimal places: Simply show the number with the specified number of digits after the decimal point, dropping any additional digits.
- Rounding to decimal places: Consider the next digit after the specified decimal place. If it's 5 or greater, round up; otherwise, round down.
For example:
- 3.45 expressed to 1 decimal place is 3.4
- 3.45 rounded to 1 decimal place is 3.5