Upper and lower bounds Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Upper and lower bounds questions. See exactly how to solve problems on upper and lower bounds, rounding to the nearest 10, rounding to the nearest cm, rounding to the nearest 100.

upper and lower boundsrounding to the nearest 10rounding to the nearest cmrounding to the nearest 100rounding to 1 decimal placerounding to the nearest 1000
GCSE Higher70 questionsStep-by-step solutions
Question 1
1 markeasy
A number nn is 4040 rounded to the nearest 1010. Write down the lower bound of nn.

Worked solution

  1. Identify the rounding

    40 to the nearest 1040 \text{ to the nearest } 10

    The true value has been rounded to the nearest 10, so it can lie up to half of 10 away.

  2. Halve the rounding unit

    102=5\frac{10}{2} = 5

    The value can be at most 5 below or 5 above the rounded figure.

  3. Subtract to find the lower bound

    40−5=3540 - 5 = 35

    The smallest value that still rounds to 40 is 35.

Answer
3535
Question 2
1 markeasy
A length is 88 cm to the nearest centimetre. Write down its upper bound.

Worked solution

  1. Identify the rounding

    8 cm to the nearest cm8\text{ cm to the nearest cm}

    Measured to the nearest centimetre, so the true length is within 0.5 cm of 8 cm.

  2. Halve the rounding unit

    12=0.5\frac{1}{2} = 0.5

    Half of 1 cm is 0.5 cm.

  3. Add to find the upper bound

    8+0.5=8.58 + 0.5 = 8.5

    Anything below 8.5 cm rounds down to 8 cm, so 8.5 cm is the upper bound.

Answer
8.5 cm8.5 \text{ cm}
Question 3
1 markeasy
A mass is 500500 g to the nearest 100100 g. Write down the lower bound.

Worked solution

  1. Identify the rounding

    500 g to the nearest 100 g500\text{ g to the nearest }100\text{ g}

    Rounded to the nearest 100 g, so the true mass is within 50 g of 500 g.

  2. Halve the rounding unit

    1002=50\frac{100}{2} = 50

    Half of 100 g is 50 g.

  3. Subtract to find the lower bound

    500−50=450500 - 50 = 450

    The least mass that rounds to 500 g is 450 g.

Answer
450 g450 \text{ g}
Question 4
1 markeasy
A length is 6.46.4 cm to 11 decimal place. Write down the upper bound.

Worked solution

  1. Identify the rounding

    6.4 cm to 1 d.p.6.4\text{ cm to }1\text{ d.p.}

    Rounded to 1 decimal place, so the true value is within 0.05 of 6.4.

  2. Halve the rounding unit

    0.12=0.05\frac{0.1}{2} = 0.05

    One decimal place means the unit is 0.1; half of it is 0.05.

  3. Add to find the upper bound

    6.4+0.05=6.456.4 + 0.05 = 6.45

    Values below 6.45 round to 6.4, so 6.45 is the upper bound.

Answer
6.45 cm6.45 \text{ cm}
Question 5
1 markeasy
The population of a town is 80008000 to the nearest thousand. Write down the least possible population.

Worked solution

  1. Identify the rounding

    8000 to the nearest 10008000 \text{ to the nearest } 1000

    Rounded to the nearest thousand, so it is within 500 of 8000.

  2. Halve the rounding unit

    10002=500\frac{1000}{2} = 500

    Half of 1000 is 500.

  3. Subtract to find the lower bound

    8000−500=75008000 - 500 = 7500

    The least population that rounds to 8000 is 7500.

Answer
75007500

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