Rounding numbers to the nearest powers of ten

Error

There was an error loading the page.

Contributors

Stanislav Duris

Feedback

From users who are members of Transition to university :

Stanislav Duris

said

Ready to use

7 years, 9 months ago

History

○

Stanislav Duris 7 years, 9 months ago

Published this.

○

Stanislav Duris commented 7 years, 9 months ago

Rounding numbers was split into 3 separate questions.

○

Stanislav Duris 7 years, 9 months ago

Gave some feedback: Ready to use

○

Stanislav Duris 7 years, 9 months ago

Created this as a copy of Rounding numbers to a given number of significant figures.

Name	Status	Author	Last Modified
Rounding numbers to a given number of significant figures	Ready to use	Stanislav Duris	20/11/2019 14:42
Rounding numbers to a given number of decimal places	Ready to use	Stanislav Duris	20/11/2019 14:42
Rounding numbers to the nearest powers of ten	Ready to use	Stanislav Duris	20/11/2019 14:42
Hannah's copy of Rounding numbers to a given number of significant figures	draft	Hannah Bartholomew	14/09/2017 11:19
Hannah's copy of Rounding numbers to a given number of significant figures	draft	Hannah Bartholomew	14/09/2017 11:28
Harry's copy of Hannah's copy of Rounding numbers to a given number of significant figures	draft	Harry Flynn	18/01/2019 14:13
Rounding: to a given number of decimal places	Ready to use	Ruth Hand	27/09/2022 09:01
Rounding: to a given number of significant figures	Ready to use	Ruth Hand	27/09/2022 09:01
ND1 Rounding DP	Ready to use	Oliver Spenceley	10/04/2024 09:26
ND2 Rounding SF (integer)	Ready to use	Oliver Spenceley	10/04/2024 09:26
ND3 Rounding SF (decimal)	Ready to use	Will Morgan	10/04/2024 09:26

There are 29 other versions that do you not have access to.

Question statement

We can approximate numbers by rounding.

Give any introductory information the student needs.

			Name	Type	Generated Value

adig	list	[ 2, 1, 6, 7, 5 ]
bdig	list	[ 1, 9, 6, 1, 4 ]
a1	integer	57615
b1	integer	41696

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(1..8), 5)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ 2, 1, 6, 7, 5 ]

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Round $\var{a1}$ to the nearest 10, 100 and 1000.

i) $\var{a1}$ rounded to the nearest 10 is: Gap 0.

ii) $\var{a1}$ rounded to the nearest 100 is: Gap 1.

iii) $\var{a1}$ rounded to the nearest 1000 is: Gap 2.

Advice

The first thing to do when we are rounding numbers is to identify the last digit we are keeping.

When you're asked to round your answer to the nearest powers of ten, you need to decide whether to keep the last digit same (rounding down) or increase it by 1 (rounding up). If the following digit is less than 5 we round down and we round up when the next digit is 5 or more.

To write it down in steps:

Identify the last digit we need to keep.
Look at the following digit.
If it's 5 or more, increase the previous digit by one.
If it's 4 or less, keep the previous digit the same.
Fill any spaces to the right of the digit with zeros if needed.

It is important to keep in mind that if the digit we are increasing is 9, it becomes zero and we increase the previous digit instead. If this digit is 9 as well, we move along to the left side until we find a digit less than 9.

This is why sometimes, the number rounded to the nearest ten is also already rounded to the nearest hundred (possibly to the nearest thousand, ten thousand...).

For example,

$295 \text{ rounded to the nearest ten is } 300 \text{. Similarly, $295$ rounded to the nearest hundred is also } 300 \text{.}$

We can see the difference between this case occuring and not occuring in parts a) and b).

a)

To approximate to the nearest ten, look at the digit in the tens column.

To round $\var{a1}$ , we look at the digit $\var{adig[1]}$ in the tens column. The following digit is $5$ , so we round up, increasing $\var{adig[1]}$ by one, becoming $\var{adig[1] +1}$ . We replace the remaining digit with $0$ . The rounded number is $\var{siground(a1, 4)}$ .

ii)

For the nearest hundred, look at the digit in the hundreds column.

Look at digit $\var{adig[2]}$ in the hundreds column. The following digit is $\var{adig[1]}$ , so we round to get $\var{siground(a1, 3)}$ .

iii)

For the nearest thousand, look at the digit in the thousands column.

Here, the digit is $\var{adig[3]}$ in the thousands column. The following digit is $\var{adig[2]}$ , so we round to get $\var{siground(a1, 2)}$ .

b)

Similarly, to round $\var{b1}$ , we look at the digit $9$ in the tens column. The following digit is more than 5, so we round up. The digit $9$ becomes $0$ and we increase the previous digit $\var{bdig[2]}$ instead. The rounded number is $\var{siground(b1, 4)}$ .

ii)

We look at $\var{bdig[2]}$ . The following digit $9$ is higher than $5$ so we round up to get $\var{siground(b1, 3)}$ .

We can see that the answer for parts i) and ii) is the same, because the digit in the tens column was 9. This is the occurence that we talked about earlier, where the nearest ten equals the nearest hundred.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Loading...

Error

Rounding numbers to the nearest powers of ten

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Stanislav Duris 7 years, 9 months ago

Stanislav Duris commented 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

a)

b)

Loading...

Error

Rounding numbers to the nearest powers of ten

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Stanislav Duris 7 years, 9 months ago

Stanislav Duris commented 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Stanislav Duris 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

a)

b)

Generated value: `list`