Answer :
To determine which statement is true among the given options by comparing the numbers, we'll carefully evaluate each statement step-by-step.
Option A: [tex]$0.098 = 0.0098$[/tex]
To check if this statement is true:
- [tex]\( 0.098 \)[/tex] is equivalent to [tex]\( \frac{98}{1000} \)[/tex].
- [tex]\( 0.0098 \)[/tex] is equivalent to [tex]\( \frac{98}{10000} \)[/tex].
Clearly, [tex]\( 0.098 \)[/tex] and [tex]\( 0.0098 \)[/tex] are not equal because [tex]\( \frac{98}{1000} \neq \frac{98}{10000} \)[/tex]. So, this statement is false.
Option B: [tex]$0.98 = 0.980$[/tex]
To check if this statement is true:
- [tex]\( 0.98 \)[/tex] and [tex]\( 0.980 \)[/tex] have different decimal notations but numerically they represent the same value because adding a zero to the end of a decimal does not change its value.
Therefore, [tex]\( 0.98 = 0.980 \)[/tex]. So, this statement is true.
Option C: [tex]$0.908 < 0.9008$[/tex]
To check if this statement is true:
- [tex]\( 0.908 \)[/tex] is equivalent to [tex]\( \frac{908}{1000} \)[/tex].
- [tex]\( 0.9008 \)[/tex] is equivalent to [tex]\( \frac{9008}{10000} \)[/tex].
Converting both to a common thousandths place:
- [tex]\( 0.908 \)[/tex] remains as [tex]\( \frac{908}{1000} \)[/tex].
- [tex]\( 0.9008 \)[/tex] in thousandths is [tex]\( \frac{9008}{10000} = 0.9008 \)[/tex].
Clearly, [tex]\( 0.908 \)[/tex] is greater than [tex]\( 0.9008 \)[/tex]. So, this statement is false.
Option D: [tex]$9.08 > 9.8$[/tex]
To check if this statement is true:
- Comparatively, [tex]\( 9.08 \)[/tex] is less than [tex]\( 9.8 \)[/tex].
So, [tex]\( 9.08 \)[/tex] is not greater than [tex]\( 9.8 \)[/tex]. This statement is false.
After evaluating all the options, the correct statement is:
B) [tex]$0.98 = 0.980$[/tex]
Option A: [tex]$0.098 = 0.0098$[/tex]
To check if this statement is true:
- [tex]\( 0.098 \)[/tex] is equivalent to [tex]\( \frac{98}{1000} \)[/tex].
- [tex]\( 0.0098 \)[/tex] is equivalent to [tex]\( \frac{98}{10000} \)[/tex].
Clearly, [tex]\( 0.098 \)[/tex] and [tex]\( 0.0098 \)[/tex] are not equal because [tex]\( \frac{98}{1000} \neq \frac{98}{10000} \)[/tex]. So, this statement is false.
Option B: [tex]$0.98 = 0.980$[/tex]
To check if this statement is true:
- [tex]\( 0.98 \)[/tex] and [tex]\( 0.980 \)[/tex] have different decimal notations but numerically they represent the same value because adding a zero to the end of a decimal does not change its value.
Therefore, [tex]\( 0.98 = 0.980 \)[/tex]. So, this statement is true.
Option C: [tex]$0.908 < 0.9008$[/tex]
To check if this statement is true:
- [tex]\( 0.908 \)[/tex] is equivalent to [tex]\( \frac{908}{1000} \)[/tex].
- [tex]\( 0.9008 \)[/tex] is equivalent to [tex]\( \frac{9008}{10000} \)[/tex].
Converting both to a common thousandths place:
- [tex]\( 0.908 \)[/tex] remains as [tex]\( \frac{908}{1000} \)[/tex].
- [tex]\( 0.9008 \)[/tex] in thousandths is [tex]\( \frac{9008}{10000} = 0.9008 \)[/tex].
Clearly, [tex]\( 0.908 \)[/tex] is greater than [tex]\( 0.9008 \)[/tex]. So, this statement is false.
Option D: [tex]$9.08 > 9.8$[/tex]
To check if this statement is true:
- Comparatively, [tex]\( 9.08 \)[/tex] is less than [tex]\( 9.8 \)[/tex].
So, [tex]\( 9.08 \)[/tex] is not greater than [tex]\( 9.8 \)[/tex]. This statement is false.
After evaluating all the options, the correct statement is:
B) [tex]$0.98 = 0.980$[/tex]
