Problem 2 - Algebra A Combined Function

Question

Write each decimal as a fraction.$$ 0.9 $$

Step-by-Step Solution

Answer

0.9 as a fraction is \( \frac{9}{10} \).

Step 1: Understand the Decimal

The decimal given is 0.9. The goal is to convert this decimal into a fraction.

Step 2: Write the Decimal as a Fraction

To convert a decimal to a fraction, identify the place value of the last digit in the decimal. Here, 9 is in the tenths place, so the fraction is \( \frac{9}{10} \).

Step 3: Simplify the Fraction

Check if the fraction \( \frac{9}{10} \) can be simplified. Since 9 and 10 have no common factors other than 1, the fraction is already in its simplest form.

Key Concepts

Decimal to Fraction Conversion

Converting a decimal into a fraction is like translating a language. Decimals, which are a way of expressing fractions, use the place value system to show the number of tenths, hundredths, thousandths, and so on. When you see a decimal like 0.9, you are looking at nine tenths.
This is because the number 9 is in the tenths place, right after the decimal point.

To convert this decimal into a fraction:

• Identify the place value of the last digit. For 0.9, the digit 9 is in the tenths place.
• Write the decimal as a fraction using this place value: 0.9 becomes \(\frac{9}{10}\).

This method of conversion is straightforward and works for any terminating decimal. Remember to always check the place of the last digit to determine your fraction's denominator.

Fraction Simplification

Once you have a fraction, like \(\frac{9}{10}\), the next step is to simplify it, if possible. Simplifying means rewriting the fraction in its most basic form, where the numerator and denominator share no common factors except for 1.

Let's take a closer look:

• Check the numerator and denominator for common factors.
• Use the greatest common factor (GCF) to divide both numerator and denominator.

For \(\frac{9}{10}\), 9 and 10 have no common factors other than 1.
Hence, the fraction is already simplified. Simplifying makes fractions easier to work with and understand.

Place Value in Decimals

The place value system is fundamental to understanding decimals. Each digit in a decimal number has a specific place value, depending on its position relative to the decimal point. This helps in converting a decimal into a fraction.

For example, examine the decimal 0.9:

• The 0 is in the ones place.
• The 9 is in the tenths place.

The position of the 9 tells us that there are 9 out of 10 possible tenths, hence \(\frac{9}{10}\).
Understanding the place value helps in correctly identifying the fraction denominators, ensuring accurate conversions for different decimals.