1.9.1 Rounding
Rounding:
Rounding a number means adjusting the digits up or down to make rough calculation easier. The result will be an estimated answer rather than a precise one.
Rounding to a place value:
To round a number to a given place value
Identify the digit in the required place value
Take a look at the digit right to that one
If this digit is less than \( 5 \), the number needs to be rounded down
If this digit is \( 5 \) or more than \( 5 \), the number needs to be rounded up
Put a zero in any following place values before the decimal
Worked example:
Round \( 1786 \) to the nearest \( 100 \)
To round \( 1786 \) to the nearest \( 100 \), the digit in the required place value is \( 7 \)
The digit right to \( 7 \) is \( 8 \) which is greater than \( 5 \), so the number will be rounded up.
\( 1786 \)→\( 1800 \)
Round \( 164321 \) to the nearest \( 1000 \)
To round \( 164321 \) to the nearest \( 1000 \), the digit in the required place value is \( 4 \)
The digit right to \( 4 \) is \( 3 \) which is less than \( 5 \), so the number will be rounded down.
\( 164321 \)→ \( 164000 \)
Rounding to a decimal place
To round a number to a given decimal place
Identify the digit in the required decimal place
Take a look at the digit right to that one
If this digit is less than \( 5 \), the number needs to be rounded down
If this digit is \( 5 \) or more than \( 5 \), the number needs to be rounded up
Make sure your answer has the required number of decimal places
Worked example:
Round \( 0.153 \) to two decimal places.
To round \( 0.153 \) to two decimal places, the digit in the required place value is \( 5 \).
The digit right to \( 5 \) is \( 3 \) which is less than \( 5 \), so the number will be rounded down.
\( 0.153 \)→\( 0.15 \)
Round \( 9.067 \) to one decimal place.
To round \( 9.067 \) to one decimal place, the digit in the required place value is \( 0 \).
The digit right to \( 0 \) is \( 6 \) which is greater than \( 5 \), so the number will be rounded up.
\( 9.067 \)→\( 9.1 \)
Rounding to significant figures
To round a number to significant figures
Find the first non-zero digit
Start counting from this number and go to the right.
Following zeros will be counted
Look at the digit right to the required significant figures
If this digit is less than \( 5 \), the number needs to be rounded down
If this digit is \( 5 \) or more than \( 5 \), the number needs to be rounded up
Worked example:
Round \( 0.06053 \) to \( 3 \) significant figures.
The first non-zero digit is \( 6 \), so is first significant figure
The two significant figures are \( 60 \)
The three significant figures are \( 605 \)
The digit right to the three significant figures \( 605 \) is \( 3 \) which is less than \( 5 \), so the number will be rounded down
\( 0.06053 \)→ \( 0.0605 \)
Round \( 69789 \) to one significant figure.
The first non-zero digit is \( 6 \), so is first significant figure
The digit right to the one significant figure \( 6 \) is \( 9 \) which is greater than \( 5 \), so the number will be rounded up
\( 69789 \)→ \( 70000 \)