UpStudy Free Solution:

To convert the decimal \(0.062\) to a fraction, follow these steps:

1. Write down the decimal divided by 1:

\[0.062 = \frac { 0.062} { 1} \]

2. Multiply both the numerator and the denominator by 1000 to eliminate the decimal point (since there are three digits after the decimal point):

\[\frac { 0.062 \times 1000} { 1 \times 1000} = \frac { 62} { 1000} \]

3. Simplify the fraction by finding the greatest common divisor (GCD) of 62 and 1000. The GCD is 2.

4. Divide both the numerator and the denominator by their GCD:

\[\frac { 62 \div 2} { 1000 \div 2} = \frac { 31} { 500} \]

So, \(0.062\) as a fraction is \(\frac { 31} { 500} \).

Supplemental Knowledge

Converting a decimal to a fraction involves several key steps, which include understanding the place value of the decimal and simplifying the resulting fraction. Here’s a deeper dive into these concepts:

1. Understanding Place Value: Each digit in a decimal number has a specific place value. For example, in the decimal \(0.062\), the digit '6' is in the hundredths place, and '2' is in the thousandths place.

2. Eliminating the Decimal Point: To convert a decimal to a fraction, you can multiply both the numerator (the decimal number) and the denominator (1) by 10 raised to the power of the number of digits after the decimal point. This shifts all digits to the left of the decimal point, effectively eliminating it.

3. Simplifying Fractions: Once you have an equivalent fraction with an integer numerator and denominator, you simplify it by dividing both by their greatest common divisor (GCD). The GCD is found by identifying the largest integer that divides both numbers without leaving a remainder.

For instance:

- Decimal: \(0.062\)

- Fraction before simplification: \(\frac { 62} { 1000} \)

- Simplified Fraction: \(\frac { 31} { 500} \)

Mastering number theory concepts such as decimals to fractions conversion is an invaluable way to advance your mathematical acumen! At UpStudy, our goal is to make learning these skills straightforward and engaging. Our platform provides comprehensive explanations across an array of subjects such as Mathematics, Chemistry, Physics and Biology--plus many others!