Converting 0.35 To A Fraction: A Step-By-Step Guide

Converting a decimal to a fraction is a fundamental mathematical skill that enhances numerical comprehension. To express 0.35 as a fraction, follow these steps:

Step 1: Express the Decimal as a Fraction

Write 0.35 as a fraction with 1 as the denominator:

$0.351\frac{0.35}{1}$

Step 2: Eliminate the Decimal Point

Since 0.35 has two digits after the decimal point, multiply both the numerator and the denominator by 100 to remove the decimal:

$0.35×1001×100=35100\frac{0.35 \times 100}{1 \times 100} = \frac{35}{100}$

Step 3: Simplify the Fraction

Identify the greatest common divisor (GCD) of 35 and 100, which is 5. Divide both the numerator and the denominator by their GCD to simplify:

$35÷5100÷5=720\frac{35 \div 5}{100 \div 5} = \frac{7}{20}$

Therefore, 0.35 as a fraction in its simplest form is $720\frac{7}{20}$ .

Verification

To confirm the accuracy, divide 7 by 20:

$\div 20 = 0.35$

This confirms that $720\frac{7}{20}$ is equivalent to 0.35.

FAQ

What is 0.35 as a fraction?
- 0.35 as a fraction in simplest form is $720\frac{7}{20}$ .
How do you convert 0.35 to a fraction?
- Write 0.35 as $0.351\frac{0.35}{1}$ , multiply numerator and denominator by 100 to get $35100\frac{35}{100}$ , then simplify to $720\frac{7}{20}$ .
Why multiply by 100 when converting 0.35 to a fraction?
- Multiplying by 100 removes the decimal point by shifting it two places to the right, converting 0.35 to 35.
What is the GCD of 35 and 100?
- The greatest common divisor of 35 and 100 is 5.
Can 0.35 be expressed as a fraction in any other form?
- While $720\frac{7}{20}$ is the simplest form, 0.35 can also be represented as $35100\frac{35}{100}$ before simplification.