The mass, 𝑥 grams, of a book is
measured as 320 grams correct to the nearest 10 grams. Write the range of possible values
So this value of 320 grams is not
the exact mass of the book. It’s been rounded. And we’re asked to work out the
range of possible values for the true mass of the book.
The nearest multiples of 10 on
either side of 320 are 310 and 330. The cut-off point for where we stop
rounding down to 310 and start rounding up to 320 is exactly halfway between these
two values, or 315. A value of 315 exactly would be
rounded up to 320, which means that 𝑥 must be greater than or equal to 315.
On the other side, the value at
which we stop rounding down to 320 and start rounding up to 330 is halfway between
these values, 325. However, a value of exactly 325
would be rounded up to 330, which means 𝑥 must be strictly less than 325. We can combine these separate
inequalities into a double-sided inequality. 𝑥 is greater than or equal to 315
and strictly less than 325.
Notice that we were told that this
value was rounded to the nearest 10 grams and the total width of this range is
10. The bounds for the edges of the
range are half of this either side. They’re both five either side of