Question

Express $\frac{7}{9}$ as a percentage, giving your answer to 2 d.p.

Short answer

Answer: The fraction $\frac{7}{9}$ is equal to 77.78% when rounded to two decimal places.

Step-by-step solution

Convert the fraction to a decimal

To convert the fraction $\frac{7}{9}$ into a decimal, divide the numerator (7) by the denominator (9). In this case, we have: $\frac{7}{9}=7÷9\approx 0.77778$ So, the fraction $\frac{7}{9}$ is approximately equal to the decimal 0.77778.

Convert the decimal into a percentage

To convert the decimal 0.77778 into a percentage, multiply it by 100: $0.77778\times 100=77.778\mathrm{\%}$

Round the percentage to two decimal places

Finally, round the percentage 77.778% to two decimal places: $77.778\mathrm{\%}\approx 77.78\mathrm{\%}$ So, the fraction $\frac{7}{9}$ is equal to 77.78% to two decimal places.

Key concepts

Fraction to Decimal Conversion

When you encounter a fraction like $\frac{7}{9}$ and need to convert it into a decimal, think of it as a division problem. The fraction line itself represents division: the top number, called the numerator, is divided by the bottom number, called the denominator.
So, when you see $\frac{7}{9}$, you perform $7÷9$. You can do this division using a calculator or by hand. When you do, you'll get approximately 0.77778.
Why is it not exact? Some fractions can't be perfectly represented as decimals and become repeating decimals. In this case, 0.77778 is rounded off for simplicity. But remember, for the sake of continued calculations, use as many decimal places as possible before the final step.

Multiplication by 100

Once you have the decimal equivalent of a fraction, in this case, 0.77778 from $\frac{7}{9}$, converting it to a percentage is straightforward.
The key step here is to multiply the decimal number by 100. Why 100? Because a percentage is simply a way of expressing a number as a part of 100.

• Percentage = Decimal × 100

So, when you multiply 0.77778 by 100, you get 77.778. This means that the fraction $\frac{7}{9}$, as a percentage, is 77.778%.
Remembering that conversion between decimal and percentage is just a shift of the decimal point, can make your calculations speedy and errors less likely.

Rounding Decimals

In the context of converting fractions to percentages, you often need to present your answer in a specific format. For example, two decimal places.
This is where rounding comes in. Rounding is adjusting a number to make it simpler while keeping its value close to what it was.
To round a number like 77.778 to two decimal places, focus on the third digit after the decimal point. If it's 5 or greater, round up the second digit; if it's less than 5, round down.

• 77.778 becomes 77.78, because the third digit "8" is more than 5.

Rounding makes numbers easier to work with and read, especially in reports or exams where precision is key but not overly exact.