What is 40/100 as a Decimal?
40/100 = 0.4
Step by step
- Simplify: 40/100 = 2/5 (divide by 20)
- Divide the numerator by the denominator: 40 ÷ 100 = 0.4
How the answer is worked out
A fraction is a division: 40/100 means 40 divided by 100, and doing that division gives 0.4. The division ends after a few digits, because the simplified denominator has no prime factors other than 2 and 5.
As a percentage, 40/100 is 40%. 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 40/100 of a cup needs 0.4 cups, about 96 millilitres.
- Measuring: 40/100 of an inch is 0.4 inches, or 10.16 millimetres.
- Money: 40/100 of a dollar is about $0.4, and 40/100 of $100 is $40.
A quicker way
The simplified denominator 5 divides 10, so scale the fraction up instead of dividing: 2/5 = 4/10 = 0.4.
Check the answer
Work backwards: 0.4 × 100 = 40, which is 40 once rounding is allowed for.
Rounding
Rounded to a whole number the decimal is 0, to one decimal place 0.4 and to two decimal places 0.40. 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: 8/85 as a decimal
- Simplify: 8/85 is already in simplest form
- Divide the numerator by the denominator: 8 ÷ 85 = 0.09411765
- The digits in brackets repeat forever: 0.0(9411764705882352)
Equivalent fractions
40/100 has the same value as 80/200, 120/300 and 400/1000: multiplying the top and bottom by the same number never changes a fraction. All of them give 0.4 when divided out.
Comparing with nearby fractions
40/100 (0.4) is bigger than 40/101 (0.396) and smaller than 41/100 (0.41). A bigger denominator means smaller pieces, so with the same numerator the fraction gets smaller.
The reciprocal
Flipping the fraction gives 100/40 = 2.5. A number multiplied by its reciprocal is always 1: 40/100 × 100/40 = 1.
In time and money
40/100 of an hour is 24 minutes, and 40/100 of a day is 9.6 hours.
In a pie chart
A slice worth 40/100 of the whole takes up 144 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:
- 40/100 in decimal form
- 40 divided by 100
- Convert 40 over 100 to a decimal
- What is 40 ÷ 100?
- 40 out of 100 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 | 0.4 |
|---|---|
| Percentage | 40% |
| Simplified | 2/5 |
| Type | proper fraction |
Related results
| 1/100 as a decimal | 1/100 = 0.01 |
| 2/100 as a decimal | 2/100 = 0.02 |
| 3/100 as a decimal | 3/100 = 0.03 |
| 41/100 as a decimal | 41/100 = 0.41 |
| 39/100 as a decimal | 39/100 = 0.39 |
The other way round: 100/40 as a decimal
Doing it in a spreadsheet
In Excel, Google Sheets or Numbers type =40/100 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
| 8/85 as a decimal | Show answer8/85 = 0.0(9411764705882352) |
| 17/93 as a decimal | Show answer17/93 = 0.(182795698924731) |
| 68/79 as a decimal | Show answer68/79 = 0.(8607594936708) |
| 70/22 as a decimal | Show answer70/22 = 3.(18) |
| 99/21 as a decimal | Show answer99/21 = 4.(714285) |
| 29/17 as a decimal | Show answer29/17 = 1.(7058823529411764) |
| 48/77 as a decimal | Show answer48/77 = 0.(623376) |
| 67/23 as a decimal | Show answer67/23 = 2.(9130434782608695652173) |
| 31/49 as a decimal | Show answer31/49 = 0.(632653061224489795918367346938775510204081) |
| 13/70 as a decimal | Show answer13/70 = 0.1(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 40/100 as a Decimal?
40/100 as a decimal is 0.4. Long-division steps and simplified fraction.
What is 40/100 as a percentage?
40%. Multiply the decimal 0.4 by 100.
What is 40/100 in simplest form?
2/5. Divide the top and bottom by their greatest common factor, 20.
Is 40/100 a terminating or a repeating decimal?
Terminating: it stops at 0.4.
What is 40/100 rounded to two decimal places?
0.40. Rounded to three places it is 0.400.
What is 40/100 of 100?
40. Multiply 100 by 40 and divide by 100, or multiply 100 by the decimal 0.4.
What is 40/100 as a ratio?
40:100, or 2:5 in simplest form. A ratio compares the part with the whole in the same way the fraction does.