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.

The first decimal place is called the 1-tenth place, that is, one out of ten or in fraction, \(\left(\frac{1}{10}\right)\),
but \(\frac{1}{10}=0.1\) which has 1 decimal place

The second decimal place is called the 1-hundredth place, that is, \(\left(\frac{1}{100}\right)\),
but \(\frac{1}{100}=0.01\) which has 2 decimal places.

The next is the 1-thousandth place, which is, \(\left(\frac{1}{1000}\right)\),
but \(\frac{1}{1000}=0.001\) which has 3 decimal places.

It goes on and on, using the same concept from the place value.

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Expressing to given Decimal Places

When expressing 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.

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Example 1

Express 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."

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Example 2

Express 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 \(\pi = 3.142\).

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For integers, expressing them to a certain number of decimal places means adding the appropriate number of zeros after the decimal point.

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Examples 2

1. 45 to 2 decimal places is 45.00.

2. 1234 to 3 decimal places is 1234.000.

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