To determine the error interval for a number, [tex]\( h \)[/tex], that has been rounded to two decimal places (d.p.) to the value 4.63, we follow these steps:
1. Identify the value - The rounded number is 4.63.
2. Determine the precision - The number is rounded to 2 decimal places, which means the precision is up to 0.01 (one hundredth).
3. Calculate the error margin:
- When a number is rounded to 2 decimal places, the maximum error margin is [tex]\( \pm 0.005 \)[/tex].
- This is because any number between [tex]\( x.625 \)[/tex] and [tex]\( x.635 \)[/tex] rounds to [tex]\( x.63 \)[/tex].
4. Establish the interval:
- The lower bound is obtained by subtracting the error margin from the rounded number: [tex]\( 4.63 - 0.005 = 4.625 \)[/tex].
- The upper bound is obtained by adding the error margin to the rounded number: [tex]\( 4.63 + 0.005 = 4.635 \)[/tex].
Thus, the error interval for the number [tex]\( h \)[/tex] is given by:
[tex]\[ 4.625 \leq h < 4.635 \][/tex]
In interval notation, this is written as:
[tex]\[ [4.625, 4.635) \][/tex]
So, the number [tex]\( h \)[/tex] lies within the interval [tex]\([4.625, 4.635)\)[/tex].
