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 bounds of a rounded number.

The bounds are the two values that the true, unrounded number must lie between. The lower bound is the smallest it could be, and the upper bound the largest it is allowed to approach.

IGCSEMathsCambridge (CIE)CoreFlashcardsNumberRounding, Estimation & Bounds

Rounding, Estimation & Bounds (Cambridge (CIE) IGCSE Maths: Core): Flashcards

Exam code: 0580 & 0980

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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 (23)

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 bounds of a rounded number.
The bounds are the two values that the true, unrounded number must lie between.
The lower bound is the smallest it could be, and the upper bound the largest it is allowed to approach.
How do you find the upper and lower bounds of a rounded number?
Halve the degree of accuracy it was rounded to, then add that half for the upper bound and subtract it for the lower bound.
For $24800$ rounded to the nearest $100$ , half of $100$ is $50$ , giving $24850$ and $24750$ .
A length $l$ has a lower bound of $3.55$ and an upper bound of $3.65$ . Complete the error interval by putting the correct inequality sign in each gap.
$3.55______l______3.65$
The completed error interval is:
$3.55 \leq l < 3.65$
The lower bound is a possible value of $l$ , but the upper bound is not, so only the first sign is inclusive.
A stick is measured as $8$ cm, to the nearest centimetre. What are its bounds?
The lower bound is $7.5$ cm and the upper bound is $8.5$ cm.
The degree of accuracy is $1$ cm, so the true length lies within $0.5$ cm either side of $8$ cm.
True or False?
The error interval for a number rounded to the nearest $100$ is wider than for one rounded to the nearest $10$ .
True.
The interval always has a width equal to the degree of accuracy itself.
So the nearest $100$ gives an interval of width $100$ , and the nearest $10$ one of width only $10$ .
How do you read the degree of accuracy from the way a rounding is described?
It may be given as a place value, so $1$ decimal place means $0.1$ and $2$ decimal places means $0.01$ .
Or it may be given as a measure, so to the nearest metre means $1$ m, and to the nearest $100$ means $100$ .

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