DECIMAL FRACTIONS: ROUNDING OFF
Outcomes
At the end of these activities you will be able to:
Round off decimal fractions to the required number of places.
Rewrite a common fraction as a decimal fraction to the required number of places.
Some questions will require you to round off an answer correct to a certain number of places,
therefore we have to learn to round off correct to the required number of decimal places.
Activity 1
Suppose you were given the following question.
Round off 8, 3654172 correct to one decimal place.
Rewrite 2/3 as a decimal fraction correct to three decimal places.
Rewrite 8, 3654172 correct to four decimal places.
Feedback:
The rule for rounding off is always look at the digits after the comma or divide the numerator by
the denominator so that we have digits after the comma. Always look at one place more than
the required number of places or divide to one place more than the required number of places. If
the digit in the extra place is 5 or 6 or 7 or 8 or 9 then add 1 to the digit before the extra digit. If
the extra digit is 0 or 1 or 2 or 3 or 4, then leave the digit before the extra as it is.
1.1 Round off 8, 3654172 correct to one decimal place.
In this case we just look. The required number of places is one. In this example we are going to
look at one more place, we will look at the second digit after the comma; therefore we will look
at the digit 6 in 8, 3653172. We don’t have to worry about the other digits: 6 is more than 5.
Therefore we increase the digit before it by 1, which means we increase 3 by 1, so 3 becomes
4. The answer is then 8,4.
Rewrite 2/3, which is same 2 ÷ 3 as a decimal fraction correct to three decimal places.
2 ÷ 3= 0,66666……
which is 0,6 recurring.
Once again we look at the fourth digit in 0,6666666….. You always look at one place more than
the required number of places. The fourth digit is 6. Therefore the third digit which is also 6 will
increase by one.
Hence the answer will be 0.667
Rewrite 8,3654172 correct to 4 decimal places.
Once again we have to look at one extra place, which means we have to look at the fifth digit
after the comma, so we look at 1 in this case. Now 1 is smaller than 5 and therefore the digit
before 1 remains the same. That means the answer is 8, 3654.
Round off to the required number of places in the table below.
QUESTION
Round off correct to
a
8,3654172
two decimal places
b
8,3654172
Three decimal places
c
8,3654172
Four decimal places
d
8,3654172
Five decimal places
e
8,3654172
Six decimal places
f
4,33333
Three decimal places
g
5,66666
Two decimal places
h
7,1111111
Five decimal places
i
8,648
One decimal places
j
8,678
One decimal place
Look at
Answer.
Answers
a) 8,3654172 = 8.37
b) 8,3654172 = 8,365
c) 8,3654172= 8,3654
d) 8,3654172=8,36542
e) 8,3654172 = 8,365417
f) 4,33333= 4,333
g) 5,66666 = 5,67
h) 7,1111111= 7,11111
i) 8,648 = 8,648
j) 8,678 = 8,7
Activity 2
Express 1/3 as a decimal fraction correct to 2 decimal places.
Use the calculator and divide 1 by 3. You get 0,3333…. Now look at third 3 in 0,3333. 3 is less
than 5. Therefore the digit before the third 3, remains the same. The answer is 0,33
Activity 3
Round off 35/7 correct to three decimal places.
Express 7/9 as a decimal fraction correct to one decimal place.
Use the calculator.
Ignore 3.
Just put 5/7 = 0,714285…. Therefore 3 5/7 = 3,714285 … Look at 8.
The 2 before 8 increases by 1. Answer 3 5/7 = 3,7143.
Use calculator 7÷9 = 0,77777…….
Look at the 2nd 7. Seven is more than 5. Therefore the 7 before the second 7 , will increase by
one. Answer 7/9 = 0,8
Complete the table below.
6.1
Express 5/9 as a decimal fraction correct to 3 decimal places.
6.2
Express 5/11 as a decimal fraction correct to 2 decimal places.
6.3
Express 7/11 as a decimal fraction correct to 1 decimal place.
6.4
Express 5 3/7 as a decimal fraction correct to 3 decimal places.
Answers
Working
6.1 5/9
Final answer
= 0,55555….
5/9 = 0,56
6.2 5/11 = 0,454545….
5/11 = 0,45
6.3 7/11 = 0,636363..
7/11= 0,6
6.4 5 3/7 = 5,428571….
5 3/7 = 5, 429
References
Bradley, T 2008, Essential Mathematics for Economics and business, 3rd edition, West Sussex
England, John Wiley and Sons.
Unisa Learner Guide-Introductory Financial Mathematics, DSC1630, 2010, Pretoria, University
of South Africa.
Unisa Learner Guide-Elementary Quantitative Methods, QMI1500, 2010, Pretoria, University of
South Africa.
Unisa Learner Guide-Quantitative Modelling 1, DSC1520, 2010, Pretoria, University of South
Africa.
Unisa Learner Guide-Introduction to Economic and Management EnvironmentB, INM 102-4,
2007, Pretoria, University of South Africa.
Developed by: D.Kooblal (Roshan), Quantitative Literacy Facilitator, Unisa (Durban), June 2013