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Chapter 4: Problem 19

Write fraction notation. Do not simplify. $$ 0.00013 $$

Short Answer

Expert verified
13/100000

Step by step solution

01

- Understand the decimal

Look at the given decimal number: 0.00013. Notice where the decimal point is and how many decimal places there are.
02

- Determine the denominator

Count the number of digits after the decimal point. There are 5 digits. This means the denominator will be 1 followed by 5 zeros, which is 100000.
03

- Write the fraction

Place the digits of the decimal number as the numerator and the determined denominator. Thus, 0.00013 can be written as 13/100000.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

fraction notation
Fraction notation is a way to express a number as the ratio of two integers. In this form, you have a numerator (top number) and a denominator (bottom number). For example, in the exercise, we converted the decimal 0.00013 into fraction notation. The result was \(\frac{13}{100000}\).
Here, 13 is the numerator and 100000 is the denominator. This notation helps us understand and work with parts of a whole more easily. When converting decimals to fractions, we focus on how many places the decimal extends, impacting the denominator.
decimal places
Decimal places are the positions of digits to the right of the decimal point in a number. Each place represents a fraction part of ten. For example, in 0.00013:
  • The first digit (1) is in the hundred thousandths place
  • The second digit (3) is in the millionths place
The number of decimal places affects how we convert a decimal into a fraction. In our case, there are 5 decimal places in 0.00013. This directly determines that our denominator will be 100000 since 5 zeros follow the 1 in the denominator.
numerator and denominator
The numerator and the denominator are the two key components of a fraction. The numerator is the top number, representing how many parts we have. The denominator is the bottom number, showing into how many parts the whole is divided.
In our exercise, when converting 0.00013 to a fraction, our numerator became 13, reflecting the significant digits of the decimal. The denominator turned out to be 100000, based on counting the decimal places. Hence, our final fraction is \(\frac{13}{100000}\). This structure makes it easier to handle calculations involving parts of a whole.

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