Question

Write each decimal as a mixed number. 1.99

Short answer

1 \(\frac{99}{100}\)

Step-by-step solution

Simplify the Decimal

Identify the whole number and the fractional part of the decimal. In the decimal 1.99, the whole number is 1, and the fractional part is 0.99.

Convert Fractional Part to a Fraction

To convert 0.99 to a fraction, write it as \(\frac{99}{100}\). This is because 0.99 is read as 'ninety-nine hundredths'.

Simplify the Fraction

Check if the fraction \(\frac{99}{100}\) can be simplified. In this case, 99 and 100 have no common factors other than 1, so the fraction is already in its simplest form.

Combine the Whole Number and the Fraction

Combine the whole number (1) and the fraction \(\frac{99}{100}\) to write the mixed number. The final answer is \(\frac{199}{100}\).

Key concepts

fractions

A fraction represents a part of a whole. It consists of two parts: a numerator and a denominator.
The numerator is the number on top, representing how many parts we have.
The denominator is the number on the bottom, indicating the total number of equal parts the whole is divided into.
For instance, in the fraction \( \frac{3}{4} \), the numerator is 3, and the denominator is 4.
This means we have 3 parts out of a total of 4 parts.
Understanding fractions is crucial because they are used in various real-life contexts, like measuring ingredients for a recipe or dividing a pizza among friends.

mixed numbers

A mixed number is a number that combines a whole number and a fraction.
For example, 1.99 can be expressed as the mixed number 1 \( \frac{99}{100} \).
The whole number part (1, in this case) represents complete units, and the fraction part (
\( \frac{99}{100} \)) represents the remaining part of the whole.
Mixed numbers are useful because they make it easier to visualize and work with quantities that are not whole.
When dealing with mixed numbers, it’s helpful to know how to add, subtract, multiply, and divide them, as these operations come up frequently in everyday life.

simplifying fractions

Simplifying fractions means reducing them to their simplest form.
This involves dividing both the numerator and the denominator by their greatest common divisor (GCD).
For instance, the fraction \( \frac{10}{20} \) can be simplified by dividing both 10 and 20 by their GCD, which is 10, resulting in \( \frac{1}{2} \).
A fraction is in its simplest form when the numerator and the denominator have no common factors other than 1.
Simplifying makes fractions easier to understand and compare.
It also assists in performing arithmetic operations more efficiently.

decimal conversion

Decimal conversion involves changing a decimal to a fraction or a mixed number.
To convert a decimal like 0.99 to a fraction, we recognize it as ninety-nine hundredths, or \( \frac{99}{100} \).
Sometimes these fractions can be simplified, but in this case, 99 and 100 have no common factors other than 1, so \( \frac{99}{100} \) is already in its simplest form.
For decimals like 1.99, we separate the whole number (1) and the decimal part (0.99).
We then convert the decimal part to a fraction and combine it with the whole number to form the mixed number 1 \( \frac{99}{100} \).
Understanding decimal conversion is essential for dealing with measurements, financial calculations, and data analysis.