Convert the following decimal numbers to fractions in their simplest form:
(a) 0.80 (b) 0.55 (c) 0.12 (d) 0.125 (e) 0.625
To 4 d.p. a number is 9.9190. State
(a) the maximum possible value,
(b) the minimum possible value of the original number.
The Correct Answer and Explanation is :
Let’s first convert the given decimal numbers to fractions in their simplest form:
(a) 0.80:
To convert 0.80 to a fraction:
[
0.80 = \frac{80}{100} = \frac{4}{5}
]
(b) 0.55:
To convert 0.55 to a fraction:
[
0.55 = \frac{55}{100} = \frac{11}{20}
]
(c) 0.12:
To convert 0.12 to a fraction:
[
0.12 = \frac{12}{100} = \frac{3}{25}
]
(d) 0.125:
To convert 0.125 to a fraction:
[
0.125 = \frac{125}{1000} = \frac{1}{8}
]
(e) 0.625:
To convert 0.625 to a fraction:
[
0.625 = \frac{625}{1000} = \frac{5}{8}
]
For the number 9.9190, to 4 decimal places:
To find the maximum possible value and minimum possible value of the original number:
(a) Maximum possible value:
When rounding a number to 4 decimal places, the last digit can vary between the number you see and the next value in the sequence. If the number is 9.9190, the maximum value would be obtained by adding the smallest possible increment that could round to 9.9190. This is just slightly more than 9.9190.
Thus, the maximum possible value is:
[
9.91905
]
This is because the next digit (the fifth decimal place) could be 5, which rounds up the fourth place to 9.9190.
(b) Minimum possible value:
For the minimum possible value, we need to subtract the smallest possible increment that would still round to 9.9190. In this case, it would be just slightly less than 9.9190, i.e., 9.91895.
Thus, the minimum possible value is:
[
9.91895
]
Explanation:
The reason for these values comes from the concept of rounding to a given number of decimal places. When a number is rounded to four decimal places, it is approximated to the nearest possible value at that precision. Therefore, the true number could have a value slightly higher or lower than the rounded value. The maximum possible value is the next smallest increment, and the minimum possible value is the previous smallest decrement, both consistent with rounding rules for decimal places.