When rounding, how do you decide whether to round up or down?

Look at the digit immediately to the right of the place you are rounding to. If it is 5 or more round up, and if it is less than 5 round down.

Why estimate a calculation you are going to work out exactly anyway?

The estimate acts as a check on the exact answer. If the exact answer turns out much bigger or much smaller than the estimate, there is a mistake in the working.

Define the lower bound of a rounded number.

The lower bound is the smallest value that would round to the given number. For example, for 24 800 to the nearest 100, the lower bound is 24 750.

How do you find the bounds of 370, given to the nearest 10?

Halve the degree of accuracy to get 10 ÷ 2 = 5, then subtract 5 for the lower bound and add 5 for the upper bound. So 370 has a lower bound of 365 and an upper bound of 375.

Define the upper bound of a rounded number.

The upper bound is the boundary value that the true number must be less than . For example, for 24 800 to the nearest 100, the upper bound is 24 850.

True or False? A number that rounds to 8, correct to 1 significant figure, has a lower bound of 7.5 and an upper bound of 8.5.

True. The degree of accuracy is 1, so the bounds are half a unit either side of 8.

A mass is 7.3 kg, correct to 1 decimal place. Why could its true value be 7.349 kg but not 7.35 kg?

The value 7.349 rounds down to 7.3, but 7.35 rounds up to 7.4. So the upper bound, 7.35 kg, is not included in the error interval.

True or False? A mass is 60 kg to the nearest 10 kg, so its upper bound is 69 kg.

False. Half of 10 kg is 5 kg, so the upper bound is 65 kg . A mass of 65 kg or more would round to 70 kg.

IGCSEMathsEdexcelMaths AFoundationFlashcards1. Numbers & the Number SystemRounding, Estimation & Error Intervals

Rounding, Estimation & Error Intervals (Edexcel IGCSE Maths A: Foundation): Flashcards

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FrontRounding to a Given Place Value
When rounding, how do you decide whether to round up or down?

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Cards in this collection (24)

When rounding, how do you decide whether to round up or down?
Look at the digit immediately to the right of the place you are rounding to.
If it is 5 or more round up, and if it is less than 5 round down.
Complete the two values that $1294$ lies between when it is rounded to the nearest $100$ :
$______< 1294 <______$
The completed line is:
$1200 < 1294 < 1300$
Counting in the units you are rounding to, here hundreds, gives the two values the number sits between.
Why do you have to take care when the digit in the place you are rounding to is a $9$ ?
Rounding a $9$ up makes it $10$ , which carries into the next place value up.
Rounding $1798$ to the nearest $10$ gives $1800$ , so the hundreds digit changes as well.
True or False?
$2.395$ rounded to $2$ decimal places should be written as $2.4$ .
False.
An answer given to $2$ decimal places has to show two digits after the point, so it must be written as $2.40$ .
Why does $1567.45$ round to $1600$ and not to $16$ ?
The zeros are place holders, keeping the $1$ and the $6$ in the thousands and hundreds columns.
Without them the number would be a hundred times too small.
How do you find the first significant figure of a number such as $0.006207$ ?
Read from the left and take the first non-zero digit, which here is the $6$ .
The zeros in front of it only show place value, so they are not significant.
Complete the sentence about the number $3097$ :
The first significant figure is $3$ , the second significant figure is $______$ , and the third significant figure is $______$ .
The completed sentence is:
The first significant figure is $3$ , the second significant figure is $0$ , and the third significant figure is $9$ .
A zero sitting between non-zero digits is counted just like any other digit.
When $0.003435$ is rounded to $3$ significant figures, why does the answer start with $0.00$ ?
Those zeros hold the significant digits in their correct place values, and they are not counted among the three significant figures.
The answer is $0.00344$ .
True or False?
When an answer is not exact and no accuracy is specified, the usual convention is to give it to $3$ significant figures.
True.
Working should be kept to at least $4$ significant figures throughout, and only the final answer rounded to $3$ .
A class of $31$ students needs at least one adult for every $10$ students. Why must $31 \div 10 = 3.1$ be rounded up?
Three adults would only be enough for $30$ students, leaving one student without an adult.
So $4$ adults are needed.
A farmer has $50$ apples and each crate holds $12$ . Why is $50 \div 12 = 4.16 \dots$ rounded down?
A fifth full crate would need $60$ apples, so only $4$ crates can be filled.
In a real situation the direction of the rounding depends on what is being counted, not on the digit after the decimal point.
What is the general rule for rounding numbers before estimating a calculation?
Round each number to $1$ significant figure, then carry out the calculation with the rounded numbers.
So $7.8$ becomes $8$ , and $1080$ becomes $1000$ .
Why estimate a calculation you are going to work out exactly anyway?
The estimate acts as a check on the exact answer.
If the exact answer turns out much bigger or much smaller than the estimate, there is a mistake in the working.
True or False?
When estimating, a small decimal such as $0.4$ should be rounded to $0$ .
False.
Rounding a value to zero destroys the calculation, and a zero underneath a fraction makes the division impossible altogether.
An estimate of $\frac{17.3 \times 3.81}{11.5}$ uses $\frac{20 \times 4}{10} = 8$ . Is $8$ an overestimate or an underestimate, and why?
$8$ is an overestimate.
The numbers on top were rounded up while the number underneath was rounded down, and both of those changes make a fraction bigger.
Complete the two rules for estimating a product $a \times b$ :
If $a$ and $b$ are both rounded up, the estimate is an $______$ .
If $a$ and $b$ are both rounded down, the estimate is an $______$ .
The completed rules are:
If $a$ and $b$ are both rounded up, the estimate is an overestimate.
If $a$ and $b$ are both rounded down, the estimate is an underestimate.
When is it better to round to something other than $1$ significant figure?
When a different value makes the arithmetic easier, such as taking $16.2$ to $15$ or $1180$ to $1200$ .
An estimate is meant to be a quick calculation you can do in your head.
Define the lower bound of a rounded number.
The lower bound is the smallest value that would round to the given number.
For example, for 24 800 to the nearest 100, the lower bound is 24 750.
How do you find the bounds of 370, given to the nearest 10?
Halve the degree of accuracy to get 10 ÷ 2 = 5, then subtract 5 for the lower bound and add 5 for the upper bound.
So 370 has a lower bound of 365 and an upper bound of 375.
Define the upper bound of a rounded number.
The upper bound is the boundary value that the true number must be less than.
For example, for 24 800 to the nearest 100, the upper bound is 24 850.
True or False?
A number that rounds to 8, correct to 1 significant figure, has a lower bound of 7.5 and an upper bound of 8.5.
True.
The degree of accuracy is 1, so the bounds are half a unit either side of 8.
A length $l$ is 3.6 km, correct to 1 decimal place. Complete its error interval in km:
$______\leq l <______$
The completed error interval, in km, is:
$3.55 \leq l < 3.65$
The lower bound is included, so it takes the $\leq$ sign, but the upper bound is not, so it takes the $<$ sign.
A mass is 7.3 kg, correct to 1 decimal place. Why could its true value be 7.349 kg but not 7.35 kg?
The value 7.349 rounds down to 7.3, but 7.35 rounds up to 7.4.
So the upper bound, 7.35 kg, is not included in the error interval.
True or False?
A mass is 60 kg to the nearest 10 kg, so its upper bound is 69 kg.
False.
Half of 10 kg is 5 kg, so the upper bound is 65 kg.
A mass of 65 kg or more would round to 70 kg.

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