When a number is rounded off, the upper bound is the highest possible value that the number could have been.
At an airport, a suitcase is weighed as 30kg rounded to the nearest 10kg.
the upper bound is halfway between 30 and 40. So the upper bound is 35kg.
Index form is another way of writing numbers, which sometimes looks neater, or simpler.
49 can be written as 72 for example, or 175,616 can be written as 563.
A number with a large index, such as 524, is a very big number. If we ever had to multiply something like 524 x 520, it would take a long time, look messy, and involve having to write out number with dozens of digits.
Luckily, we have discovered special rules which can make the calculation much easier. Provided the base number is the same, we can just add the indices together
e.g. 524 x 520 = 524+20 = 544
This doesn’t work if the base numbers are different
e.g. 524 x 720 is NOT 544, or 3544, or 1244
In algebra, we can do the same thing, provided the letter is the same:
e.g. y15 x y10 = y15+10 = y25
If we are dividing numbers in index form, we can subtract the indices.
e.g. y15 ÷ y10 = y15-10 = y5
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