NUMBER AND ALGEBRA „ß2%!,ß.5-"%23
UNDERSTANDING
5 Write
a
b
c
1
8
as a decimal. Using this value, find:
3
as a decimal.
8
7
as a decimal.
8
1
as a decimal.
16
REASONING
6 Consider these fractions:
1 1 1 1 1 1 1 1
, , , , , , ,
2 3 4 5 6 7 8 9
REFLECTION
Without performing any division, you can see that
1 1 1
, , and 1 will produce terminating decimals,
2 4 5
while
8
1 1 1
, ,
3 6 7
and
1
9
will produce repeating decimals.
Explain how this can be seen, and write a general
statement to determine whether a fraction will produce
a terminating or repeating decimal.
If you need to choose between
a fraction and a decimal, when
is a fraction a better choice
and when is a decimal a better
choice?
Rounding and repeating decimals
6C
Rounding
■
■
■
When rounding decimals, look at the first digit past the number of decimal places required.
If this digit is less than 5, write the number with the required number of decimal places.
If this digit is 5 or more, add one to the digit in the last decimal place being kept.
WORKED EXAMPLE 10
Round the following to 2 decimal places.
a 3.641 883
b 18.965 402 0
THINK
a
b
WRITE
1
Write the number and underline the required
decimal place.
2
Circle the next digit and round according to the rule.
Note: Since the circled digit is less than 5, we leave
the number as it is.
1
Write the number and underline the required
decimal place.
2
Circle the next digit and round according to the rule.
Note: Since the circled digit is greater than or
equal to 5, add 1 to the last decimal place that is
being kept.
■
■
192
a
3.641 883
= 3.64 1 883
ö 3.64
b
18.965 402 0
= 18.96 5 402 0
ö 18.97
If you need to add 1 to the last decimal place and the digit in this position is a 9, the result is 10.
The 0 is put in the last required place and the 1 is added to the digit in the next place to the left.
0.298 rounded to 2 decimal places is 0.30.
Maths Quest 7 for the Australian Curriculum
NUMBER AND ALGEBRA „ß2%!,ß.5-"%23
WORKED EXAMPLE 11
Round the following to the number of decimal places shown in the brackets.
a 27.462 973 (4)
b 0.009 94 (3)
THINK
a
WRITE
1
Write the number and underline the required
decimal place.
2
Circle the next digit and round according to
the rule.
Note: Since the circled digit is greater than 5,
add 1 to the last decimal place that is being
kept. As 1 is being added to 9, write 0 in the
last place and add 1 to the previous digit.
b Repeat steps 1 and 2 of part a.
a
27.462 973
= 27.462 9 7 3
ö 27.4630
b
0.009 94
= 0.009 9 4
ö 0.010
WORKED EXAMPLE 12
Round 8.672 to the nearest unit.
THINK
1
2
WRITE
Write the decimal and think of the number with
the whole number part only.
Look at the first digit after the decimal point and,
if it is greater than or equal to 5, add 1 to the
whole number.
■
8.672
ö9
When trying to answer Worked example 12, you can think of the question as: ‘Is 8.672 closer
to 8 or 9?’
WORKED EXAMPLE 13
Melinda had $51.67 in her bank account. She wanted to withdraw all her money so the bank
rounded the amount to the nearest 5 cents. How much money did the teller give to Melinda?
THINK
1
2
3
Write the actual amount she had in her account.
Determine whether the last digit is closer to 5 or
closer to 10, then rewrite the approximate value.
Note: Alternatively it can be seen that 67 cents is
closer to 65 cents than 70 cents.
Write a sentence.
WRITE
$51.67
ö $51.65
Melinda will receive $51.65 from the bank.
Chapter 6
Decimals
193