What is .625 as a fraction in its simplest form and how do you work it out?
To convert a decimal to a fraction, divide the numbers after the decimal point by 10 to the power of the quantity of numbers after the decimal.
The decimal number 0.625 has the number 625 after the decimal point and as there are 3 numbers after the decimal point, 10 to the power of 3 gives 1,000.
Therefore, the decimal in fractional form would initially look like this:
$$ \frac{625}{1000} $$
This is the decimal $0.625$ in its initial fractional form, but can you reduce both numbers to simpler terms?
How To Reduce A Fraction
Reducing a fraction means dividing both the numerator and denominator by a common factor. This changes the appearance of the fraction, but not its value.
If you can find the highest common factor (HCF), you can simplify the fraction in one step. Otherwise, you can divide by smaller common factors repeatedly.
Step 1: Find All Factors Of Both Numbers
What are the factors of 625 and 1,000?
$$ 625 = {1, 5, 25, 125, 625} \ 1000 = {1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 125, 200, 250, 500, 1000} $$
The shared common factors are ${1, 5, 25, 125}$, with the highest being $125$.
Step 2A: Using Highest Common Factor
To reduce the fraction using the highest common factor, divide both numbers by 125:
$$ \begin{array} \frac{625 \div 125}{1000 \div 125} & & \text{divide by HCF $125$} \ \frac{5}{8} \end{array} $$
Therefore, $0.625$ in its simplest fractional form is $\frac{5}{8}$.
Step 2B: Using Smaller Common Factors
If the highest common factor is not obvious, you can reduce gradually using smaller factors.
A) Both numbers share a factor of 5:
$$ \begin{array} \frac{625 \div 5}{1000 \div 5} & & \text{divide by $5$} \ \frac{125}{200} \end{array} $$
B) Again, divide both by 5:
$$ \begin{array} \frac{125 \div 5}{200 \div 5} & & \text{divide by $5$} \ \frac{25}{40} \end{array} $$
C) Again, divide both by 5:
$$ \begin{array} \frac{25 \div 5}{40 \div 5} & & \text{divide by $5$} \ \frac{5}{8} \end{array} $$
Now, since there are no more common factors between 5 and 8, the fraction is fully simplified.
Step 3: Check Your Fraction
To verify, convert the fraction $\frac{5}{8}$ back to a decimal using short division.
Set up the division:
| 0 | . | 6 | 2 | 5 | |
|---|---|---|---|---|---|
| 8 | $\cancel{5}$ | . | $\cancel{^5!0}$ | $\cancel{^2!0}$ | $\cancel{^4!0}$ |
- $8 \div 5 = 0$ remainder $5$
- $8 \div 50 = 6$ remainder $2$
- $8 \div 20 = 2$ remainder $4$
- $8 \div 40 = 5$ remainder $0$
Result: $0.625$ — the original decimal. ✅
Summary
The decimal number $.625$ can be expressed as the fraction $\frac{5}{8}$.
To perform this conversion, express the decimal as a fraction over 1000, then reduce using either the highest common factor or smaller common factors step-by-step.
Next, try your hand at converting $.375$ as a fraction.