What is 42/45 as a Decimal?
42/45 = 0.9(3)
Step by step
- Simplify: 42/45 = 14/15 (divide by 3)
- Divide the numerator by the denominator: 42 ÷ 45 = 0.93333333
- The digits in brackets repeat forever: 0.9(3)
How the answer is worked out
A fraction is a division: 42/45 means 42 divided by 45, and doing that division gives 0.9(3). 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, 42/45 is 93.3333%. It is a proper fraction, so its value is between 0 and 1, and it is more 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 42/45 of a cup needs 0.933 cups, about 224 millilitres.
- Measuring: 42/45 of an inch is 0.9333 inches, or 23.71 millimetres.
- Money: 42/45 of a dollar is about $0.93, and 42/45 of $100 is $93.33.
A quicker way
Long division: 45 goes into 42 0 times, remainder 42.
Bring down a zero: 420 ÷ 45 = 9, remainder 15.
Bring down a zero: 150 ÷ 45 = 3, remainder 15.
The remainder 15 has come up before, so the digits from that point repeat forever: 0.9(3).
Check the answer
Work backwards: 0.933333 × 45 = 42, which is 42 once rounding is allowed for.
Rounding
Rounded to a whole number the decimal is 1, to one decimal place 0.9 and to two decimal places 0.93. 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: 9/16 as a decimal
- Simplify: 9/16 is already in simplest form
- Divide the numerator by the denominator: 9 ÷ 16 = 0.5625
Equivalent fractions
42/45 has the same value as 84/90, 126/135 and 420/450: multiplying the top and bottom by the same number never changes a fraction. All of them give 0.9(3) when divided out.
Comparing with nearby fractions
42/45 (0.9333) is bigger than 42/46 (0.913) and smaller than 43/45 (0.9556). A bigger denominator means smaller pieces, so with the same numerator the fraction gets smaller.
The reciprocal
Flipping the fraction gives 45/42 = 1.0(714285). A number multiplied by its reciprocal is always 1: 42/45 × 45/42 = 1.
In time and money
42/45 of an hour is 56 minutes, and 42/45 of a day is 22.4 hours.
In a pie chart
A slice worth 42/45 of the whole takes up 336 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:
- 42/45 in decimal form
- 42 divided by 45
- Convert 42 over 45 to a decimal
- What is 42 ÷ 45?
- 42 out of 45 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 | 0.9(3) |
|---|---|
| Percentage | 93.3333% |
| Simplified | 14/15 |
| Type | proper fraction |
Related results
| 1/45 as a decimal | 1/45 = 0.0(2) |
| 2/45 as a decimal | 2/45 = 0.0(4) |
| 3/45 as a decimal | 3/45 = 0.0(6) |
| 43/45 as a decimal | 43/45 = 0.9(5) |
| 41/45 as a decimal | 41/45 = 0.9(1) |
The other way round: 45/42 as a decimal
Doing it in a spreadsheet
In Excel, Google Sheets or Numbers type =42/45 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
| 9/16 as a decimal | Show answer9/16 = 0.5625 |
| 3/80 as a decimal | Show answer3/80 = 0.0375 |
| 4/77 as a decimal | Show answer4/77 = 0.(051948) |
| 99/91 as a decimal | Show answer99/91 = 1.(087912) |
| 94/89 as a decimal | Show answer94/89 = 1.(05617977528089887640449438202247191011235955) |
| 73/53 as a decimal | Show answer73/53 = 1.(3773584905660) |
| 38/36 as a decimal | Show answer38/36 = 1.0(5) |
| 72/55 as a decimal | Show answer72/55 = 1.3(09) |
| 82/56 as a decimal | Show answer82/56 = 1.46(428571) |
| 6/59 as a decimal | Show answer6/59 = 0.(1016949152542372881355932203389830508474576271186440677966) |
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 42/45 as a Decimal?
42/45 as a decimal is 0.9(3). Long-division steps and simplified fraction.
What is 42/45 as a percentage?
93.3333%. Multiply the decimal 0.933333 by 100.
What is 42/45 in simplest form?
14/15. Divide the top and bottom by their greatest common factor, 3.
Is 42/45 a terminating or a repeating decimal?
Repeating: 0.9(3). The digits in brackets go on forever.
What is 42/45 rounded to two decimal places?
0.93. Rounded to three places it is 0.933.
What is 42/45 of 100?
93.3333. Multiply 100 by 42 and divide by 45, or multiply 100 by the decimal 0.933333.
What is 42/45 as a ratio?
42:45, or 14:15 in simplest form. A ratio compares the part with the whole in the same way the fraction does.