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 an error interval .

An error interval is the range of values a number could have had before it was rounded or truncated. It is written using inequalities.

GCSEMathsEdexcelFoundationFlashcardsNumberRounding, Estimation & Error Intervals

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

Exam code: 1MA1

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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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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 an error interval.
An error interval is the range of values a number could have had before it was rounded or truncated.
It is written using inequalities.
A stick has length $l$ cm, given as $5$ cm to the nearest whole number. What is the error interval for $l$ ?
The interval runs from $4.5$ to $5.5$ :
$4.5 \leq l < 5.5$
Notice that the rounded value $5$ sits exactly at the midpoint of the interval.
In an error interval, why is one end written with $\leq$ and the other with $<$ ?
The lower end is a possible value, because a number sitting exactly there rounds up to the stated value.
The upper end is not possible, because a number sitting exactly there would round up to the next value instead.
The first $3$ digits of an answer $a$ have been written down as $2.95$ . What is the error interval for $a$ ?
The interval is $2.95 \leq a < 2.96$ .
Truncating simply cuts the extra digits off, so a truncated value is the smallest value in its interval rather than the middle of it.
The length of a road, $l$ km, is given as $3.6$ , correct to $1$ decimal place. Complete the error interval:
$______\leq l <______$
The completed error interval is:
$3.55 \leq l < 3.65$
The degree of accuracy is $0.1$ km, so the interval reaches half of that, $0.05$ , either side of $3.6$ .
True or False?
A mass given as $14$ kg has the same error interval whether it was rounded or truncated to $2$ significant figures.
False.
Truncated, the interval is $14 \leq m < 15$ , but rounded it is $13.5 \leq m < 14.5$ .

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