# Upper and Lower Bounds (1)

This worksheet is about writing upper and lower bounds as inequalities.

Key stage:  KS 4

Curriculum topic:  Number

Curriculum subtopic:  Apply/Interpret Limits of Accuracy When Rounding/Truncating

Difficulty level:

### QUESTION 1 of 10

This worksheet is about lower and upper bounds.

Suppose we've rounded a number to the nearest whole number and get 14.

Numbers that round up to 14 include 13.9, 13.75, 13.694, 13.5. The smallest of these is 13.5. This is called the LOWER BOUND.

Anything smaller will round down to 13.

Larger numbers that round down to 14 include 14.1, 14.34968, 14.49. The largest of these is 14.4999999... This is the UPPER BOUND, which we write as 14.5.

We write these bounds as an inequality.

13.5 ≤ n < 14.5

Note: The lower bound is included in the inequality, but the upper bound is not – it would round up.

Example

Find the upper and lower bounds for 8500 which has been rounded to the nearest hundred.

8499, 8470, 8450 would round up.

8450 is the smallest, so this is the LOWER BOUND.

8501, 8548, 8549 would round down.

8549.999999 is the largest, so we say that 8550 is the UPPER BOUND.

8450 ≤ n < 8550

The number n has been rounded to the nearest whole number, to get 76.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 75.9 75.5 76.5 76.9 Lower Upper

The number n has been rounded to the nearest whole number, to get 16.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 15.49 15.5 16.49 16.5 Lower Upper

The number n has been rounded to the nearest whole number, to get 52.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 51 51.5 52 52.5 Lower Upper

The number n has been rounded to the nearest thousand, to get 73 000.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 72 999 72 500 73 500 73 005 Lower Upper

The number n has been rounded to the nearest thousand, to get 8000.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 7500 8500 7995 8005 Lower Upper

The number n has been rounded to the nearest hundred, to get 8000.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 7500 8050 8500 7950 Lower Upper

The number n has been rounded to the nearest ten, to get 8000.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 8005 8500 7500 7995 Lower Upper

The number n has been rounded to the nearest whole number, to get 8000.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 7999 7999.5 8050 8000.5 Lower Upper

The number n has been rounded to the nearest hundred, to get 8500.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 8595 8550 8450 8495 Lower Upper

The number n has been rounded to the nearest ten, to get 8500.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 8450 8495 8545 8505 Lower Upper
• Question 1

The number n has been rounded to the nearest whole number, to get 76.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 75.9 75.5 76.5 76.9 Lower Upper
• Question 2

The number n has been rounded to the nearest whole number, to get 16.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 15.49 15.5 16.49 16.5 Lower Upper
• Question 3

The number n has been rounded to the nearest whole number, to get 52.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 51 51.5 52 52.5 Lower Upper
• Question 4

The number n has been rounded to the nearest thousand, to get 73 000.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 72 999 72 500 73 500 73 005 Lower Upper
• Question 5

The number n has been rounded to the nearest thousand, to get 8000.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 7500 8500 7995 8005 Lower Upper
• Question 6

The number n has been rounded to the nearest hundred, to get 8000.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 7500 8050 8500 7950 Lower Upper
• Question 7

The number n has been rounded to the nearest ten, to get 8000.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 8005 8500 7500 7995 Lower Upper
• Question 8

The number n has been rounded to the nearest whole number, to get 8000.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 7999 7999.5 8050 8000.5 Lower Upper
• Question 9

The number n has been rounded to the nearest hundred, to get 8500.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.

 8595 8550 8450 8495 Lower Upper
• Question 10

The number n has been rounded to the nearest ten, to get 8500.

A and B are the upper and lower bounds for n, such that  A ≤ n < B.

Select the correct values for A and B, the lower and upper bounds.