Decimal places refer to the number of digits to the right of the decimal point.
Examples:
1. 12.34567 has 5 decimal places.
2. 100.004 has 3 decimal places.
but \(\frac{1}{10}=0.1\) which has 1 decimal place
but \(\frac{1}{100}=0.01\) which has 2 decimal places.
but \(\frac{1}{1000}=0.001\) which has 3 decimal places.
It goes on and on, using the same concept from the place value.
When rounding a number to a specified number of decimal places:
1. First count the number of decimal places required.
2. Then round-off the next digit after the last required decimal place.
If the digit is among
the numbers (0 - 4), round it down to 0, but if it is among (5 to 9), round it up, that is add
1 to the last required decimal place.
3. Then add or remove trailing zeros if needed to match the exact number of decimal places.
Example 1
Round 5.6789 to 2 decimal places
Solution
2 decimal places mean, the 1-tenth and the 1-hundredth places, which have the digits 6 and 7 respectively. We will therefore consider the digit at the 1-thousandth place, which is 8.
8 is amongst the digits 5 to 9, hence we need to round it up by adding 1 to the last digit of our required deicmal place. That is \(7+1\).
Hence, \(5.6789 \approx 5.68\) to 2 decimal places.
Note:
\(\approx\) this symbol is read "Approximately."
Example 2
Round 3.14159 to 3 decimal places.
Solution
Three decimal places mean we are considering the numbers in the 1-tenth, 1-hundredth and the 1-thousandth places. These digits are 1, 4 and 1 respectively. We therefore need to look at the number in the 10-thousandth place (which is the number, 5).
5 is among the numbers (5 to 9) hence we need to round it up by adding 1 to the last digit in our 3 required decimal places, which is 1. So we have \(1 + 1 =2\)
Hence, \(3.14159 \ \approx 3.142\)
Note:
Remember that \(\pi = 3.142\).
For integers, expressing them to a certain number of decimal places mean adding the appropriate number of zeros after the decimal point.
Examples 2
1. 45 to 2 decimal places is 45.00.
2. 1234 to 3 decimal places is 1234.000.
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