what is 5 1/8% in decimal? note it is a mixed number with percentage. please show a solution
The Correct Answer and Explanation is:
Answer:
518 %=0.051255 \tfrac{1}{8}\,\% = 0.05125
When a percentage is written as a mixed number you have to untangle two ideas:
- The mixed-number part, which combines several whole percents with a fractional piece.
- The percent sign itself, which means “divide by 100.”
1. Turn the mixed number into one fraction
For 5185 \tfrac{1}{8} the denominator is 8, so convert the 5 wholes into eighths and add: 518=5+18=5×88+18=40+18=418.5 \tfrac{1}{8}=5+\frac{1}{8} =\frac{5\times8}{8}+\frac{1}{8} =\frac{40+1}{8} =\frac{41}{8}.
So we are dealing with 418\tfrac{41}{8} percent.
2. Remove the percent sign
Because “percent” literally means “out of 100,” replace the symbol with ÷ 100: 418 %=418×1100=41800.\frac{41}{8}\,\%=\frac{41}{8}\times\frac{1}{100} =\frac{41}{800}.
Now the quantity is an ordinary fraction.
3. Convert the fraction to decimal
Divide 41 by 800 (long division or a calculator): 41800=0.05125.\frac{41}{800}=0.05125.
Making sense of the result
- Ball-park check. Five percent equals 0.05. The answer 0.05125 is slightly larger, exactly what we expect after adding one-eighth of a percent (0.00125).
- Place-value perspective. The 5 sits in the hundredths place (0.05 …), matching five percent. The trailing “125” reaches into the ten-, hundred-, and thousand-thousandths places, highlighting how small a fraction of a percent really is.
- Algebraic pattern. Any mixed-number percent abca \tfrac{b}{c}% becomes
(a+bc)%=ac+bc×100,\Bigl(a+\frac{b}{c}\Bigr)\%=\frac{a c+b}{c\times100},
the same three-step recipe used above: merge, divide by 100, then (if desired) convert the resulting fraction into a decimal.
Therefore, 5185 \tfrac{1}{8}% expressed as a decimal is 0.05125\boxed{0.05125}.
Such fluency guards against costly misreads in finance, statistics, and science, where a misplaced percent symbol or decimal point can change conclusions drastically. Mastery of this conversion thus reinforces both numerical confidence and real-world accuracy and clarity.
