What is 24/84 as a Decimal?
24/84 = 0.(285714)
Step by step
- Simplify: 24/84 = 2/7 (divide by 12)
- Divide the numerator by the denominator: 24 ÷ 84 = 0.28571429
- The digits in brackets repeat forever: 0.(285714)
How the answer is worked out
A fraction is a division: 24/84 means 24 divided by 84, and doing that division gives 0.(285714). The division never ends, because the simplified denominator has a prime factor other than 2 or 5. The digits in brackets repeat forever.
As a percentage, 24/84 is 28.5714%. It is a proper fraction, so its value is between 0 and 1, and it is less than one half.
Why calculate this?
Decimals are easier to compare and to use in calculators and spreadsheets than fractions.
- Cooking: a recipe that asks for 24/84 of a cup needs 0.286 cups, about 68.5714 millilitres.
- Measuring: 24/84 of an inch is 0.2857 inches, or 7.26 millimetres.
- Money: 24/84 of a dollar is about $0.29, and 24/84 of $100 is $28.57.
A quicker way
Long division: 84 goes into 24 0 times, remainder 24.
Bring down a zero: 240 ÷ 84 = 2, remainder 72.
Bring down a zero: 720 ÷ 84 = 8, remainder 48.
Bring down a zero: 480 ÷ 84 = 5, remainder 60.
Bring down a zero: 600 ÷ 84 = 7, remainder 12.
Bring down a zero: 120 ÷ 84 = 1, remainder 36.
Keep going until a remainder repeats; from then on the digits repeat as well.
Check the answer
Work backwards: 0.285714 × 84 = 24, which is 24 once rounding is allowed for.
Rounding
Rounded to a whole number the decimal is 0, to one decimal place 0.3 and to two decimal places 0.29. Round only at the end: rounding halfway through a calculation can change the last digit.
The formula explained
decimal = numerator ÷ denominator. The numerator is the top number and counts the pieces; the denominator is the bottom number and says how many equal pieces make a whole. Dividing the top by the bottom gives the size of the fraction as a decimal.
Another worked example: 5/91 as a decimal
- Simplify: 5/91 is already in simplest form
- Divide the numerator by the denominator: 5 ÷ 91 = 0.05494505
- The digits in brackets repeat forever: 0.(054945)
Equivalent fractions
24/84 has the same value as 48/168, 72/252 and 240/840: multiplying the top and bottom by the same number never changes a fraction. All of them give 0.(285714) when divided out.
Comparing with nearby fractions
24/84 (0.2857) is bigger than 24/85 (0.2824) and smaller than 25/84 (0.2976). A bigger denominator means smaller pieces, so with the same numerator the fraction gets smaller.
The reciprocal
Flipping the fraction gives 84/24 = 3.5. A number multiplied by its reciprocal is always 1: 24/84 × 84/24 = 1.
In time and money
24/84 of an hour is 17.14 minutes, and 24/84 of a day is 6.86 hours.
In a pie chart
A slice worth 24/84 of the whole takes up 102.86 degrees of the circle, because a full turn is 360 degrees. That is the angle to draw when you make the chart by hand with a protractor.
Other ways to ask this
The same calculation is often asked in other words. All of these have the answer above:
- 24/84 in decimal form
- 24 divided by 84
- Convert 24 over 84 to a decimal
- What is 24 ÷ 84?
- 24 out of 84 as a decimal number
Terms used on this page
- Numerator: the top number of a fraction.
- Denominator: the bottom number, the number of equal parts in a whole.
- Terminating decimal: a decimal that ends, such as 0.25.
- Repeating decimal: a decimal whose digits repeat forever, such as 0.333….
The answer in other forms
| Decimal | 0.(285714) |
|---|---|
| Percentage | 28.5714% |
| Simplified | 2/7 |
| Type | proper fraction |
Related results
| 1/84 as a decimal | 1/84 = 0.01(190476) |
| 2/84 as a decimal | 2/84 = 0.0(238095) |
| 3/84 as a decimal | 3/84 = 0.03(571428) |
| 25/84 as a decimal | 25/84 = 0.29(761904) |
| 23/84 as a decimal | 23/84 = 0.27(380952) |
The other way round: 84/24 as a decimal
Doing it in a spreadsheet
In Excel, Google Sheets or Numbers type =24/84 into any cell. Replace the numbers with cell references (for example A1 and B1) to reuse the formula for a whole column.
Common mistakes
Dividing the denominator by the numerator flips the fraction. A bar over (or brackets around) digits means they repeat forever.
Practice examples
| 5/91 as a decimal | Show answer5/91 = 0.(054945) |
| 82/93 as a decimal | Show answer82/93 = 0.(881720430107526) |
| 83/69 as a decimal | Show answer83/69 = 1.(2028985507246376811594) |
| 28/69 as a decimal | Show answer28/69 = 0.(4057971014492753623188) |
| 85/35 as a decimal | Show answer85/35 = 2.(428571) |
| 11/24 as a decimal | Show answer11/24 = 0.458(3) |
| 19/7 as a decimal | Show answer19/7 = 2.(714285) |
| 76/99 as a decimal | Show answer76/99 = 0.(76) |
| 77/93 as a decimal | Show answer77/93 = 0.(827956989247311) |
| 85/56 as a decimal | Show answer85/56 = 1.517(857142) |
How this answer was calculated
The result is worked out from the numbers in this page's address when the page is opened, using exact arithmetic wherever possible and rounding only for display. Nothing is copied from a printed table. If you think an answer is wrong, please tell us through the contact page and we will check it.
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Questions
What is 24/84 as a Decimal?
24/84 as a decimal is 0.(285714). Long-division steps and simplified fraction.
What is 24/84 as a percentage?
28.5714%. Multiply the decimal 0.285714 by 100.
What is 24/84 in simplest form?
2/7. Divide the top and bottom by their greatest common factor, 12.
Is 24/84 a terminating or a repeating decimal?
Repeating: 0.(285714). The digits in brackets go on forever.
What is 24/84 rounded to two decimal places?
0.29. Rounded to three places it is 0.286.
What is 24/84 of 100?
28.5714. Multiply 100 by 24 and divide by 84, or multiply 100 by the decimal 0.285714.
What is 24/84 as a ratio?
24:84, or 2:7 in simplest form. A ratio compares the part with the whole in the same way the fraction does.