how to turn . 0156 into a fraction

Question

UpStudy AI · Accepted Answer

To convert the decimal **0.0156** into a fraction, follow these steps:

### Step 1: Write the Decimal as a Fraction
Place the decimal over its place value. Since there are four digits after the decimal point, the place value is ten thousand.

$$
0.0156 = \frac{156}{10,000}
$$

### Step 2: Simplify the Fraction
Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and then dividing both by that number.

**Find the GCD of 156 and 10,000:**

1. **Factorize 156:**
   $$
   156 = 2 \times 2 \times 3 \times 13 = 2^2 \times 3 \times 13
   $$

2. **Factorize 10,000:**
   $$
   10,000 = 10^4 = (2 \times 5)^4 = 2^4 \times 5^4
   $$

3. **Identify Common Factors:**
   Both numbers have the factor $$2^2$$.

4. **GCD:**
   $$
   \text{GCD} = 2^2 = 4
   $$

**Divide both numerator and denominator by the GCD:**

$$
\frac{156}{10,000} = \frac{156 \div 4}{10,000 \div 4} = \frac{39}{2,500}
$$

### Step 3: Final Answer
The simplified fraction form of **0.0156** is:

$$
\frac{39}{2,500}
$$

### Verification

To ensure the fraction is correct, you can divide the numerator by the denominator:

$$
\frac{39}{2,500} = 0.0156
$$

This confirms that **0.0156** is equivalent to **$$\frac{39}{2,500}$$**.
To convert **0.0156** to a fraction, write it as **$$\frac{156}{10,000}$$** and simplify to **$$\frac{39}{2,500}$$**.

how to turn . 0156 into a fraction

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