rounding problem solving gcse

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Rounding GCSE Questions PDF

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This revision resource contains lots of practice rounding to a given level of accuracy, including rounding: decimals to the nearest integer, to the nearest ten, hundred and thousand, 1, 2 and 3 decimal places and 1 significant figure. Questions are abstract or based on real-life scenarios such as speeds, populations, etc.

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Bounds ( AQA GCSE Maths )

Revision note.

Bounds & Error Intervals

What are bounds.

• It simply means how low or high the number could have been before it was rounded

How do we find bounds when a number has been rounded?

• UPPER BOUND – To find the upper bound add on half the degree of accuracy
• LOWER BOUND – To find the lower bound take off half the degree of accuracy
• ERROR INTERVAL: LB ≤ x < UB
•  the upper bound is the cut off point for the greatest value that the number could have been rounded from but will not actually round to the number itself
• The degree of accuracy is 10 (rounding to 3 s.f. here requires rounding to the nearest ten)
• Half the degree of accuracy is 5

How do we find bounds when a number has been truncated?

• This means that the UPPER BOUND is found by adding 1 to the digit in the place value that the number was truncated to
• The LOWER BOUND is always the number the value was truncated to
• For example, the error interval for the number 1230, truncated to 3 significant figures will be 1230 ≤  x < 1240

Worked example

The degree of accuracy is 1 decimal place, or 0.1 km so the true value could be up to 0.05 km above or below this

Upper bound:

3.6 + 0.05 = 3.65 km

Lower bound:

3.6 - 0.05 =  3.55 km

Upper bound: 3.65 km Lower bound: 3.55 km

Calculations using Bounds

How do i find the bounds of a calculation.

• The upper bound of  T can be found by adding together the upper bound of a and the upper bound of  b
• The lower bound of T can be found by adding together the lower bound of a and the lower bound of  b
• The upper bound of  T can be found by using the upper bound of a and subtracting the lower bound of b
• The lower bound of T can be found by using the lower bound of a and subtracting the upper bound of b
• The upper bound of  T can be found by multiplying together the upper bound of a and the upper bound of  b
• The lower bound of T can be found by multiplying together the lower bound of a and the lower bound of  b
• The upper bound of  T can be found by using the upper bound of a and dividing it by the lower bound of b
• The lower bound of T can be found by using the lower bound of a and dividing it by the upper bound of b

How can bounds help with calculations?

• You can use bounds to calculate the level of accuracy of a calculation
• e.g. If the lower bound of an value is 8.33217... and the upper bound is 8.33198...
• The true value is between 8.33217... and 8.33198...
• Both bounds round to 8.332 to 4sf
• To 5sf they differ (first is 8.3322 and second is 8.3320)
• Therefore you know the answer is definitely rounds to 8.332 to 4 significant figures

(a) A room measures 4 m by 7 m, where each measurement is made to the nearest metre

Find the upper and lower bounds for the area of the room

Find the bounds for each dimension, you could write these as error intervals, or just write down the upper and lower bounds As they have been rounded to the nearest metre, the true values could be up to 0.5 m bigger or smaller

Calculating the lower bound of the area, using the two smallest measurements

3.5 × 6.5 =

Lower Bound = 22.75 m 2

Calculating the upper bound of the area, using the two largest measurements

4.5 × 7.5 =

Upper Bound = 33.75 m 2

(b) David is trying to work out how many slabs he needs to buy in order to lay a garden path.

Slabs are 50 cm long, measured to the nearest 10 cm.

The length of the path is 6 m, measured to the nearest 10 cm.

Find the maximum number of slabs David will need to buy.

Find the bounds for each measurement, you could write these as error intervals, or just write down the upper and lower bounds As they have been rounded to the nearest 10 cm, the true values could be up to 5 cm bigger or smaller

We have a mixture of centimetres and metres, so it is useful to change them both to metres for later calculations

The maximum number of slabs needed will be when the path is as long as possible (6.05 m), and the slabs are as short as possible (0.45 m)

Assuming we can only purchase whole slabs

The maximum number of slabs to be bought is 14

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Author: Dan

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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Rounding of Numbers Explained for the 11+ Exams!

1. what is rounding of numbers.

Rounding off makes the number simple by keeping its value intact but closer to the next number. Many physical quantities like the amount of money, distance covered, length measured, etc are estimated by rounding off the actual number to the nearest possible whole number. For example:

• £29.99 could be rounded to £30.
• 57 minutes could be rounded to an hour.

1.1 Rounding of Whole and Decimal Numbers

We follow the below steps while rounding whole numbers and decimals:

• Observe the next smaller place value i.e towards the right of the digit that is being rounded off. For example, for rounding to the nearest hundred, observe the digit in the tens place.
• If the digit in the smaller place value is less than 5, then we round down. To round down, replace all the digits after the digit that you are rounding to by 0.
• If the digit in the smaller place value is greater than or equal to 5, then we round up. To round up, add one to the digit that you are rounding to and replace all the digits after it with 0.

1.2 Rounding Off - Example

Example: Round the following numbers to nearest ten:

• Identify the digit in the tens place: 1 Look at the digit to the right  of the digit to be rounded: 3 Work out whether to round up or round down: If the digit to the right is greater than or equal to 5, then round up the digit. Otherwise, round down the digit. Here, 3 < 5 i.e. round down. So, the digit to be rounded (1) remains unchanged. Every other digit after it becomes zero. Answer is 410
• Identify the digit in the tens place: 9 Look at the digit to the right  of the digit to be rounded: 9 Work out whether to round up or round down: If the digit to the right is greater than or equal to 5, then round up the digit. Otherwise, round down the digit. Here, 9 > 5 i.e. round up. So, 9 + 1 = 10, and this 1 is carried over to the hundreds place to give 3 + 1 = 4 Every other digit after it becomes zero. Answer is 400

Example: Round 9460 to the nearest thousand.

Solution: Consider thousands place and follow the steps as given below:

Work out which digit  you need to round: 9 Look at the digit to the right  of the digit to be rounded: 4 Work out whether to round up or round down: If the digit to the right is greater than or equal to 5, then round up the digit. Otherwise, round down the digit. Every other digit after it becomes zero. Answer is 9000

Example: Round 0.93 to the nearest tenth.

Solution: Work out which digit  you need to round: 9 Look at the digit to the right  of the digit to be rounded: 3 Work out whether to round up or round down: If the digit to the right is greater than or equal to 5, then round up the digit. Otherwise, round down the digit. Here, 3 < 5 i.e. round down. So, the digit to be rounded (9) remains unchanged. Every other digit after it becomes zero. Answer is 0.9

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Rounding Decimals Worksheet

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Help your students prepare for their Maths GCSE with this free Rounding Decimals worksheet of 44 questions and answers

• Section 1 of the Rounding Decimals worksheet contains 36 skills-based questions, in 3 groups to support differentiation
• Section 2 contains 4 applied Rounding Decimals questions with a mix of worded problems and deeper problem solving questions
• Section 3 contains 4 foundation and higher level GCSE exam style Rounding Decimals questions 
• Answers and a mark scheme for all Rounding Decimals questions
• Follows variation theory with plenty of opportunities for students to work independently at their own level
• All questions created by fully qualified expert secondary maths teachers
• Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards

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Raise maths attainment across your school with hundreds of flexible and easy to use GCSE maths worksheets and lessons designed by teachers for teachers.

Rounding decimals at a glance

Rounding decimals involves approximating a decimal number to make it easier to read and work with. It is common to round decimals to the nearest whole number, nearest tenth, nearest hundredth or nearest thousandth. 

In order to round decimal numbers, we can picture where the number would appear on a number line to help us decide whether to round up or down. In general numbers 5 or greater round up and numbers 4 or less round down. For example, when rounding numbers to 2 decimal places, we look at the next decimal place value, the thousandths. If the number in the thousandths column is 5 or greater we round up. If it is 4 or less we round down. 

As an alternative to rounding to a given number of decimal places, we could round to a given number of significant figures.

Looking forward, students can then progress to additional number worksheets , for example an equivalent fractions & ordering fractions worksheet or simplifying fractions worksheet .

For more teaching and learning support on Number our GCSE maths lessons provide step by step support for all GCSE maths concepts.

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Rounding reasoning & problem solving

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

2 October 2016

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great activity.

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Great thanks - really good to get my LA Yr5er thinking.

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This is a great problem solving activity on problem solving, thanks

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