Websink Prep UKKS3 MathsYear 8 chaptersMaths textbooksReceptionYear 1Year 2Year 4Year 5Year 6Year 3Year 7Year 8Year 9GCSEBrowse allPast papersFind a tutorBecome a tutor
KS3 Maths · Year 8Chapter 2 · Surds, rounding and bounds
Year 8 · Chapter 2

Surds, rounding and bounds

By the end of this chapter you will be able to

  • Round to decimal places, to the nearest 10, 100 or 1000, and to significant figures
  • Estimate the answer to a calculation by rounding each number to 1 significant figure
  • Recognise square and cube numbers, and find their roots; estimate a square root between two whole numbers
  • Simplify a surd by taking out the largest square factor, and add or multiply simple surds
  • Write the lower and upper bounds of a measurement that has been rounded, and use them for sums

You should already know

  • Place value and rounding to the nearest 10, 100 and 1000 (Year 7)
  • Square numbers and cube numbers, and their factors (Year 7, Chapter 3)
  • Decimals and the place value of decimal digits (Year 7)

Where this leads

  • Rationalising denominators and exact trigonometric values (GCSE)
  • Upper and lower bounds in calculations with two or more measures, areas and volumes (Year 9)
  • Using surds and irrational numbers in Pythagoras and geometry (Year 8, Chapter 9)

National Curriculum for England, Key Stage 3 mathematics, Year 8. Content: Round to a given number of decimal places or significant figures, Estimate answers and check calculations by rounding, Use square and cube roots, and simplify simple surds such as sqrt 12 = 2 sqrt 3, Find upper and lower bounds of a rounded measurement, including the sum of two rounded lengths.

Exercise P  Do you remember?

Non-calculator
1
FWhat is 9 × 9?
2
FWhat is 5 × 5 × 5?
3
FRound 6.3 to the nearest whole number.
4
FWork out 0.4 × 10.
5
FWhich is a square number: 18, 25, 30 or 40?
2.1

Rounding to decimal places and to the nearest 10, 100 or 1000

Year 8
Round to a given number of decimal places or to the nearest 10, 100 or 1000
Video lesson: Rounding to decimal places and to the nearest 10, 100 or 1000Coming soon
A school trip costs £3,456 for the bus, and the head teacher wants the total in hundreds of pounds for the newsletter. She rounds it to the nearest hundred, so parents see about £3,500.

Rounding makes a number simpler, so it is easier to read or to use in a quick check. We round to a given place.

To round to a place, look at the digit just after that place. If it is 5 or more, round up. If it is 4 or less, leave the digit as it is.

Key ideas

  • Look at the digit after the place you are rounding to.
  • 5 or more: round up. 4 or less: keep the digit.
  • Round to decimal places (dp) by keeping the digits up to that place.
  • Round to the nearest 10, 100 or 1000 by finding the multiples either side, then the halfway point.
Worked example 2.1.1
Round 3.76 to 1 decimal place.

Method. Look at the digit after the 1 decimal place. It decides whether to round up.

  1. Find the digit to round to. We keep 1 decimal place.
    3.76
  2. Look at the next digit. The digit after the 1 decimal place is 6. It is 5 or more, so round up.
    next digit = 6
  3. Write the answer.
    3.8

Check. The answer 3.8 is close to 3.76, and it has 1 decimal place.

Watch out. Do not stop at the first digit after the point. Look only at the one digit after the last one you keep.

Worked example 2.1.2
Round 0.04685 to 3 decimal places.

Method. Look at the digit after the 3 decimal places. It decides whether to round up.

  1. Find the digit to round to. We keep 3 decimal places.
    0.04685
  2. Look at the next digit. The digit after the 3 decimal places is 8. It is 5 or more, so round up.
    next digit = 8
  3. Write the answer.
    0.047

Check. The answer 0.047 is close to 0.04685, and it has 3 decimal places.

Watch out. Do not stop at the first digit after the point. Look only at the one digit after the last one you keep.

Worked example 2.1.3
Round 3,456 to the nearest 100.

Method. Round to the nearest 100. Find the two multiples of 100 either side of 3,456.

  1. Find the multiples either side. The multiples of 100 near 3,456 are 3,400 and 3,500.
    3,400 < 3,456 < 3,500
  2. Find the halfway point. Halfway between 3,400 and 3,500 is 3,450.
    3,400 + 50 = 3,450
  3. Compare with the halfway point. 3,456 is at or above 3,450, so round up.
    3,456 ≥ 3,450
  4. Write the answer.
    3,500

Check. 3,500 is a multiple of 100, and it is the closest one to 3,456.

Watch out. When the digit is 5 or more, round up. For example 3,456 to the nearest 100 is 3,500, not 3,400.

Watch out

Watch out: do not round the first digit and forget the rest. 3.749 rounded to 1 dp is 3.7, because the next digit is 4. It is not 3.8.

Exam tip

Exam tip. Write the number with the place you are rounding to underlined before you decide. That helps you see the next digit.

Exercise 2A  Rounding to places

Non-calculator
1
FRound 3.76 to 1 decimal place.
2
FRound 45.649 to 2 decimal places.
3
FRound 7.342 to 1 decimal place.
4
FRound 0.04685 to 3 decimal places.
5
FRound 6.5 to 0 decimal places.
6
FRound 3,456 to the nearest 10.
7
FRound 3,456 to the nearest 100.
8
FRound 5,678 to the nearest 1000.
9
FRound 72,455 to the nearest 1000.
10
RSam says that 4.449 rounded to 2 decimal places is 4.44. Is Sam right? Explain how you know.
11
PSThe length of a garden is 14.66 m. Round it to 1 decimal place.
12
PSA recipe needs 2.345 kg of flour. Round this to 2 decimal places.
13
PSA town has 27,850 people. Give this number to the nearest 100.
14
RRound 3.14159 to 3 decimal places. Then round the original number to 2 decimal places.
2.2

Significant figures

Year 8
Round to a given number of significant figures
Video lesson: Significant figuresComing soon
Priya measured the length of a bridge as 2 348 metres, but her GPS only needs 3 significant figures for the map. She writes 2 350 m.

The significant figures (sf) of a number start at the first non-zero digit. Zeros at the start are not significant. Zeros in the middle are significant.

To round to n significant figures, count n digits from the first non-zero digit, then look at the next digit. Round up if it is 5 or more.

Key ideas

  • The first non-zero digit is the first significant figure.
  • Zeros at the start (such as in 0.0523) are not significant.
  • Zeros at the end of a whole number may be placeholders, so keep them to show the size.
  • Round up if the next digit is 5 or more.
Worked example 2.2.1
Round 3,452 to 3 significant figures.

Method. Count 3 significant figures from the first non-zero digit, then look at the next digit.

  1. Find the first non-zero digit. Zeros at the start do not count as significant figures.
    3452
  2. Keep 3 significant figures. Round so that there are 3 digits from the first non-zero digit.
    3 sf
  3. Write the answer. Keep the zeros needed to show the place value.
    3,450

Check. 3,450 has 3 significant figures and is close to 3452.

Watch out. Zeros in the middle count as significant figures. Zeros at the start do not.

Worked example 2.2.2
Round 0.004567 to 3 significant figures.

Method. Count 3 significant figures from the first non-zero digit, then look at the next digit.

  1. Find the first non-zero digit. Zeros at the start do not count as significant figures.
    0.004567
  2. Keep 3 significant figures. Round so that there are 3 digits from the first non-zero digit.
    3 sf
  3. Write the answer. Keep the zeros needed to show the place value.
    0.00457

Check. 0.00457 has 3 significant figures and is close to 0.004567.

Watch out. Zeros in the middle count as significant figures. Zeros at the start do not.

Worked example 2.2.3
Round 47,650 to 2 significant figures.

Method. Count 2 significant figures from the first non-zero digit, then look at the next digit.

  1. Find the first non-zero digit. Zeros at the start do not count as significant figures.
    47650
  2. Keep 2 significant figures. Round so that there are 2 digits from the first non-zero digit.
    2 sf
  3. Write the answer. Keep the zeros needed to show the place value.
    48,000

Check. 48,000 has 2 significant figures and is close to 47650.

Watch out. Zeros in the middle count as significant figures. Zeros at the start do not.

Watch out

Watch out: 0.0503 to 2 significant figures is 0.050, not 0.05. The zero is kept to show that the number has 2 significant figures.

Exam tip

Exam tip. Count significant figures from the first non-zero digit. Do not count the zeros at the start.

Exercise 2B  Rounding to significant figures

Non-calculator
1
FRound 3452 to 3 significant figures.
2
FRound 6789 to 2 significant figures.
3
FRound 0.004567 to 3 significant figures.
4
FRound 47650 to 2 significant figures.
5
FRound 2.0996 to 3 significant figures.
6
FRound 123456 to 4 significant figures.
7
PSA bag holds 0.0426 kg of rice. Give this mass to 2 significant figures.
8
RLena says that 0.0500 has 3 significant figures. Is she right? Explain how you know.
9
RRound 0.00039821 to 2 significant figures. Explain why the answer has two zeros after the point.
10
PSA tin has a volume of 375 cm3. Round the volume to 1 significant figure.
11
PSThe mass of a planet is 5.9726 × 1024 kg. Give this mass to 2 significant figures.
12
RRound 6.9 to 1 significant figure. Then round 6.9 to the nearest whole number. Are the answers the same?
13
PSRound 0.6349 to 2 significant figures. How many decimal places is that?
14
RRound 987.6 to 2 significant figures. Then write the answer as an ordinary number.
2.3

Square roots, cube roots and estimating

Year 8
Use square and cube roots, Estimate answers and check calculations by rounding
Video lesson: Square roots, cube roots and estimatingComing soon
Amira is planning a square vegetable plot. The plot has an area of 144 m2, so each side is √144 = 12 m. She estimates the cost of the fence by rounding the numbers first.

The square root of a number is the number that multiplied by itself gives that number. √49 = 7, because 7 × 7 = 49.

The cube root of a number is the number that multiplied by itself three times gives that number. The cube root of 27 is 3, because 3 × 3 × 3 = 27. The symbol is ∛.

To estimate a calculation, round each number to 1 significant figure, then work it out. The answer is only an estimate, but it tells you if your exact answer is about right.

Key ideas

  • A square root is the number that was squared: √49 = 7.
  • A cube root is the number that was cubed: ∛27 = 3.
  • To estimate, round each number to 1 significant figure first.
  • If a square root is not a whole number, find the two whole numbers it lies between.
Worked example 2.3.1
Find √144.

Method. Find the number that multiplied by itself gives 144.

  1. Think of square numbers. We look for a number that multiplied by itself gives 144.
    12 × 12 = 144
  2. Check the square numbers either side. 11 × 11 = 121 and 13 × 13 = 169, so 144 is exactly 12 squared.
    121 < 144 = 122 < 169
  3. Write the root. The square root of 144 is 12.
    √144 = 12

Check. 12 × 12 = 144, so the square root is right.

Watch out. A square root is the number that was squared. Check by multiplying the answer by itself.

Worked example 2.3.2
Find ∛216.

Method. Find the number that multiplied by itself three times gives 216.

  1. Think of cube numbers. We need a number with 6 × 6 × 6 = 216.
    6 × 6 × 6 = 216
  2. Check the cube numbers either side. 5 cubed is 125 and 7 cubed is 343, so 216 sits exactly on 6 cubed.
    125 < 216 = 63 < 343
  3. Write the root. The cube root of 216 is 6.
    ∛216 = 6

Check. 6 cubed is 216, which is 216.

Watch out. A cube root is the number that was cubed. Check by multiplying the answer by itself, then by itself again.

Worked example 2.3.3
Estimate 48.7 × 0.31 by rounding each number to 1 significant figure.

Method. Round each number to 1 significant figure, then do the calculation with the rounded numbers.

  1. Round each number to 1 significant figure. Keep only the first non-zero digit, and make the rest zeros.
    48.7 → 50 and 0.31 → 0.3
  2. Work out the calculation with the rounded numbers. Multiply the rounded numbers: 50 × 0.3.
    50 × 0.3 = 15
  3. Write the estimate. This is the answer we expect, close to the exact answer.
    15

Check. The estimate 15 is close to the exact answer, so it is a sensible check.

Watch out. Round to 1 significant figure, not to a whole number. For 48.7 use 50, not 49.

Watch out

Watch out: √(ab) is not the same as √a + √b. For example √(9 + 16) = √25 = 5, but √9 + √16 = 3 + 4 = 7.

Exam tip

Exam tip. When you estimate, say which rounded numbers you used. Examiners look for the working, not only the answer.

Exercise 2C  Square roots, cube roots and estimates

Non-calculator
1
FWork out √144.
2
FWork out √289.
3
FWork out √2,025.
4
FWork out ∛216.
5
FWork out ∛1,000.
6
FBetween which two consecutive whole numbers does √50 lie?
7
FEstimate 61.8 × 0.49 by rounding each number to 1 significant figure. Give your estimate.
8
FEstimate 612 ÷ 19.8 by rounding each number to 1 significant figure.
9
RLisa calculates 52 × 0.49 = 255. Use an estimate to show that her answer is wrong.
10
PSFind ∛1000 + ∛8.
11
PSThe area of a square tile is 81 cm2. Find the side length of the tile.
12
PSA cube has a volume of 343 cm3. Find the side length of the cube.
13
REstimate √50 + √30 to the nearest whole number. Use the whole numbers each root lies between.
14
RExplain why √50 is not a whole number. Accept any answer that says 50 is not a square number, so its square root is between 7 and 8.
2.4

Simplifying surds

Year 8
Simplify simple surds such as √12 = 2√3, Add and multiply simple surds
Video lesson: Simplifying surdsComing soon
A square garden has an area of 12 m2. Its side is √12 metres long. Noah says the side is exactly 2√3 m, which is about 3.46 m. He does not need a calculator to check this.

A surd is a root that cannot be written as a whole number, such as √2 or √12. We keep surds in exact form.

To simplify a surd, find the largest square number that divides the number under the root. Then split the root:

√12 = √(4 × 3) = √4 × √3 = 2√3

Surds with the same number under the root can be added, just like like terms: 3√2 + 5√2 = 8√2.

To multiply surds, multiply the numbers under the root: √2 × √8 = √16 = 4.

Key ideas

  • √a × √b = √(ab), and √(ab) = √a × √b.
  • Find the largest square factor (4, 9, 16, 25, 36 ...) to simplify a surd.
  • You can only add surds that have the same number under the root.
  • A surd that is a whole number, such as √9 = 3, is not a surd any more.
Worked example 2.4.1
Simplify √12.

Method. Find the largest square number that is a factor of the number under the root, then take its square root outside.

  1. Look for the largest square factor. We want a square number, such as 4, 9, 16 or 25, that divides 12.
    12 = 4 × 3
  2. Split the surd. √12 = √4 × √3, and √4 = 2.
    √12 = √4 × √3 = 2√3
  3. Write the answer. The part under the root is now square-free (3 has no square factors).
    2√3

Check. Check: (2√3)2 = 22 × 3 = 4 × 3 = 12, which is right.

Watch out. Use the largest square factor. √12 can be split in more than one way, but you must keep splitting until no square factor is left.

Worked example 2.4.2
Simplify √50.

Method. Find the largest square number that is a factor of the number under the root, then take its square root outside.

  1. Look for the largest square factor. We want a square number, such as 4, 9, 16 or 25, that divides 50.
    50 = 25 × 2
  2. Split the surd. √50 = √25 × √2, and √25 = 5.
    √50 = √25 × √2 = 5√2
  3. Write the answer. The part under the root is now square-free (2 has no square factors).
    5√2

Check. Check: (5√2)2 = 52 × 2 = 25 × 2 = 50, which is right.

Watch out. Use the largest square factor. √50 can be split in more than one way, but you must keep splitting until no square factor is left.

Worked example 2.4.3
Work out √3 × √12.

Method. Multiply the numbers under the roots, then simplify the answer.

  1. Multiply the numbers under the roots. √3 × √12 = √(3 × 12).
    √36
  2. Find the square root. 36 is a square number, so its square root is a whole number.
    √36 = 6
  3. Write the answer.
    6

Check. √3 × √12 is about 6.0, and 6 is about 6.

Watch out. Only multiply the numbers under the same kind of root. Do not add them.

Watch out

Watch out: √12 is not 2√6, and it is not 4√3. The largest square factor of 12 is 4, so √12 = 2√3.

Exam tip

Exam tip. Square your answer to check it. (2√3)2 = 4 × 3 = 12, which is right.

Exercise 2D  Simplifying and using surds

Non-calculator
1
FSimplify √8.
2
FSimplify √18.
3
FSimplify √27.
4
FSimplify √48.
5
FSimplify √75.
6
FSimplify √128.
7
FWork out √3 × √12.
8
FWork out √6 × √2. Give your answer in its simplest form.
9
FSimplify 3√2 + 5√2.
10
PSSimplify √12 + √3. Give your answer as a surd in its simplest form.
11
PSSimplify √75 + √27. Give your answer as a surd in its simplest form.
12
RIs √10 rational or irrational? Explain how you know.
13
PSShow that √(4 × 5) = 2√5.
14
RWork out √2 × √8 + √18. Give your answer in its simplest form.
2.5

Upper and lower bounds

Year 8
Find upper and lower bounds of a rounded measurement, Use bounds for a sum of two rounded measurements
Video lesson: Upper and lower boundsComing soon
A builder measures a shelf as 1.2 m, to the nearest 0.1 m. The shelf might be a little shorter or a little longer. Bounds show the smallest and biggest lengths the shelf could really be.

When a measurement is rounded, the true value could be anywhere in a range. The lower bound is the smallest value that would round to the measurement. The upper bound is the value just above the largest one. The upper bound is not included.

To find the bounds, subtract and add half the rounding unit. For 1.2 m to 1 decimal place, the rounding unit is 0.1, so half is 0.05. The bounds are 1.15 and 1.25, so 1.15 ≤ length < 1.25.

Key ideas

  • Lower bound: subtract half the rounding unit. It is included (≤).
  • Upper bound: add half the rounding unit. It is not included (<).
  • For a sum, add the lower bounds, and add the upper bounds.
  • Use the bounds, not the rounded values, when you add measurements.
Worked example 2.5.1
A length is 6.4 cm, correct to 1 decimal place. Write the bounds of the length.

Method. The value 6.4 is rounded to 1 decimal place. Find the half-unit either side.

  1. Find the unit of rounding. The last place is 0.1.
    unit = 0.1
  2. Find half of the unit. Half of the rounding unit is the most the value can be away from the rounded answer.
    0.1 ÷ 2 = 0.05
  3. Find the lower and upper bounds. Subtract half a unit for the lower bound and add half a unit for the upper bound.
    6.4 − 0.05 = 6.35 and 6.4 + 0.05 = 6.45
  4. Write the answer. The upper bound is not included, so use < for it.
    6.35 ≤ x < 6.45

Check. Both 6.35 and values just below 6.45 round to 6.4, so the bounds are right.

Watch out. The lower bound is included (≤). The upper bound is not included (<). Do not round the bounds again.

Worked example 2.5.2
A mass is 3 kg, correct to the nearest kilogram. Write the bounds.

Method. The value 3 is rounded to 0 decimal places. Find the half-unit either side.

  1. Find the unit of rounding. The last place is 1.
    unit = 1
  2. Find half of the unit. Half of the rounding unit is the most the value can be away from the rounded answer.
    1 ÷ 2 = 0.5
  3. Find the lower and upper bounds. Subtract half a unit for the lower bound and add half a unit for the upper bound.
    3 − 0.5 = 2.5 and 3 + 0.5 = 3.5
  4. Write the answer. The upper bound is not included, so use < for it.
    2.5 ≤ x < 3.5

Check. Both 2.5 and values just below 3.5 round to 3, so the bounds are right.

Watch out. The lower bound is included (≤). The upper bound is not included (<). Do not round the bounds again.

Worked example 2.5.3
Two lengths are 3.4 m and 2.6 m, each correct to 1 decimal place. Find the bounds of their total length.

Method. For a sum, add the two lower bounds to find the lower bound, and add the two upper bounds to find the upper bound.

  1. Find the bounds of the first length. 3.4 rounded to 1 dp.
    3.35 ≤ x < 3.45
  2. Find the bounds of the second length. 2.6 rounded to 1 dp.
    2.55 ≤ y < 2.65
  3. Add the lower bounds. The smallest total comes from the two smallest values.
    3.35 + 2.55 = 5.90
  4. Add the upper bounds. The largest total (not included) comes from the two upper bounds.
    3.45 + 2.65 = 6.10
  5. Write the answer.
    5.90 ≤ total < 6.10

Check. The total is between 5.90 and 6.10; the width is 0.20, which is the sum of the two widths.

Watch out. Use the bounds, not the rounded values, when you add. The width of the answer is the two widths added.

Watch out

Watch out: the upper bound is not included. A length of 6.45 cm can round up to 6.5 cm, but the upper bound 6.45 is where the range stops. Write the range as 6.35 ≤ length < 6.45 carefully.

Exam tip

Exam tip. Write the inequality with ≤ for the lower bound and < for the upper bound. Examiners give marks for the correct symbols.

Exercise 2E  Bounds of rounded measurements

Non-calculator
1
FA measurement x is 6.4, correct to 1 decimal place. Write the lower and upper bounds of x.
2
FA measurement x is 3, correct to the nearest whole number. Write the lower and upper bounds of x.
3
FA measurement x is 0.7, correct to 1 decimal place. Write the lower and upper bounds of x.
4
FA measurement x is 4.25, correct to 2 decimal places. Write the lower and upper bounds of x.
5
FA measurement x is 9, correct to the nearest whole number. Write the lower and upper bounds of x.
6
PSA length x is 8 cm, correct to the nearest cm. Write the bounds of x. What is the largest value x can take, and is it included?
7
RA rope is 2.3 m long, correct to 1 decimal place. Can the rope be 2.35 m long? Explain your answer.
8
RA jug holds 1.5 litres, correct to 1 decimal place. Write the bounds of the volume x. Explain why the upper bound is not included.
9
PSTwo pieces of wood are 4.5 m and 3.2 m long, each correct to 1 decimal place. Write the bounds of their total length.
10
PSTwo pieces of wire are 6.8 cm and 2.1 cm long, each correct to 1 decimal place. Write the bounds of their total length.
11
RA bag of sugar weighs 500 g, correct to the nearest 10 g. Explain why the lower bound is 495 g.
12
PSThe length of a field is 120 m, correct to the nearest 10 m. Write the bounds of its length.
13
RAli says that a length of 6.5 cm, correct to 1 decimal place, can be 6.55 cm. Is Ali right? Explain how you know.

Chapter summary

SkillMethod
Round to a placeLook at the digit after the place: 5 or more round up, 4 or less keep the digit
Round to significant figuresCount from the first non-zero digit, then look at the next digit
Square and cube rootsThe number that was squared (√) or cubed (∛) to give the number
EstimateRound each number to 1 significant figure, then calculate
Simplify a surdTake out the largest square factor, then split the root: √12 = 2√3
Add and multiply surdsAdd only surds with the same root; √a × √b = √(ab)
BoundsLower bound = value − half the unit (≤). Upper bound = value + half the unit (<).

Can you…?

  • I can round to decimal places, to the nearest 10, 100 or 1000, and to significant figures
  • I can find square roots and cube roots of perfect squares and cubes
  • I can estimate roots between two whole numbers, and estimate calculations
  • I can simplify a surd by taking out the largest square factor
  • I can add and multiply simple surds
  • I can write the lower and upper bounds of a rounded measurement

Key terms

significant figure
a digit that counts, starting from the first non-zero digit
surd
a root that does not give a whole number, such as √2
rational number
a number that can be written as a fraction, such as 3/4 or √16
irrational number
a number that cannot be written as a fraction, such as √2
lower bound
the smallest value that rounds to the given value
upper bound
the value just above the largest possible value (not included)
estimate
a rough answer found by rounding the numbers first

Exercise 2Z  Check-up

Non-calculator
1
Round 5.672 to 2 decimal places.
2
Round 48,765 to the nearest 1000.
3
Round 0.07382 to 2 significant figures.
4
Work out ∛64.
5
Between which two consecutive whole numbers does √70 lie?
6
Simplify √72.
7
Work out √5 × √10.
8
Simplify 4√3 + 2√3.
9
A length is 4.7 cm, correct to 1 decimal place. Write the lower and upper bounds.
10
Estimate 39.8 × 0.21 by rounding each number to 1 significant figure.

Total 27 marks. Allow about 27 minutes.

Exercise 2X  Exam-style questions

Non-calculator
1
FA mass x is 2.5 kg, correct to 1 decimal place. Write the bounds of x.[2 marks]
2
FSimplify √28.[2 marks]
3
FRound 0.004 982 to 3 significant figures.[2 marks]
4
FShow that √48 + √12 = 6√3.[3 marks]
5
FTwo sides of a rectangle are 5.6 cm and 3.2 cm, each correct to 1 decimal place. Write the bounds of the total of the two sides.[3 marks]
6
FA length is 15 cm, correct to the nearest cm. Write the bounds of the length, and explain why the upper bound is not included.[3 marks]
7
FEstimate 589 ÷ 28.9 by rounding each number to 1 significant figure. Give your estimate.[3 marks]
8
FWrite 2 345 678 to 3 significant figures.[2 marks]
9
FThe area of a square is 50 cm2. Find the side length, giving your answer as a surd in its simplest form.[4 marks]
10
FExplain why √36 is rational but √35 is irrational. Accept any answer that says 36 is a square number (6 × 6), but 35 is not.[3 marks]
← Chapter 1: Indices and standard formChapter 3: Fractions and percentages →

Websink Prep UK is an independent site. It is not affiliated with, endorsed by or sponsored by AQA, Pearson Edexcel, OCR, WJEC, Eduqas, CCEA, SQA, GL Assessment, CEM or the Department for Education. All exam board names and trademarks belong to their owners. Past papers are linked from the exam boards' own websites and are not hosted here.

About Websink Prep UK · Find a tutor · Privacy · Terms · Cookie settings