The mass of the remaining cake can be obtained straightforwardly by getting the difference of the masses of the whole cake and the cake slice:
[tex]mass \ of \ remaining \ cake \ = mass \ of \ whole \ cake \ - \ mass \ of \ one \ slice[/tex]
Sorting the given and plugging them into the equation would give:
[tex]mass \ of \ remaining \ cake \ = 0.870 \ kg - 0.1151 \ kg\\\\\\\boxed {mass \ of \ remaining \ cake = 0.7549 \ kg}[/tex]
The problem requires that the answer be expressed with the correct number of significant figures. To do so, recall the rules for determining the number of significant figures needed:
The final answer must have the same number of decimal places as the given with the least number of decimal places.
The final answer must have the same number of significant figures as the given with the least number of significant figures.
Based on the rules above, the final answer to this problem must have 3 decimal places since the given with the least number of decimal places has 3 (0.870 kg). The last digit is 4 (0.7549 kg) and is followed by the digit 9, hence, it will be increased by one. Based on the rounding rule, the final answer must be:
[tex]\boxed {\boxed {mass \ of \ remaining \ cake \ = 0.755 \ kg}}[/tex]
The mass of the remaining cake is [tex]\boxed{0.755{\text{ kilogram}}}.[/tex]
Further explanation:
Given:
Mass of the whole cake is [tex]0.870{\text{ kg}}.[/tex]
The mass of the slice is [tex]0.1151{\text{ kg}}.[/tex]
Explanation:
The given mass of the whole cake is [tex]0.870{\text{ kg}}.[/tex]
The given mass of the slice is [tex]0.1151{\text{ kg}}.[/tex]
The mass of the remaining cake can be obtained as follows,
[tex]\boxed{{\text{Mass of remaining cake}} = {\text{Mass of whole cake}} - {\text{Mass of one slice}}}[/tex]
Substitute 0.870 for whole mass of cake and 0.1151 for mass of one slice.
[tex]\begin{aligned}{\text{Mass of remaining cake}} &= {\text{Mass of whole cake}} - {\text{Mass of one slice}}\\&= 0.870 - 0.1151\\&= 0.7459\\&= 0.755\\\end{aligned}[/tex]
The mass of the cake in three significant figure is [tex]0.755{\text{ kg}}.[/tex]
Hence, the mass of the remaining cake is [tex]\boxed{0.755{\text{ kilogram}}}.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Significant Figures
Keywords: significant figures, mass, cake, slice, bakery, measured, whole cake, customer, bought one slice, one slice, mass of slice, 0.1151 kg, mass of cake 0.870, remaining cake, kilograms, remaining mass of cake.
